Over the summer, the Greenwich Country Day School sent out an invitation for its annual Cider and Donuts event. To emphasize its commitment to diversity, the school noted that the autumn gathering was open to families “who identify as Black, Asian, Latinx, multiracial, indigenous, Middle Eastern, and/or people of color.”But to the alarm of the local Republican Town Committee, the invitation left out a demographic not often thought of as marginalized in this affluent community.“You listed nearly every group but white people … was that on purpose?” the committee asked in an Instagram post. “Is that how you bring people together? Inclusion …?”Stunned, the private school’s administrator graciously said the letter could have more clearly conveyed that all were welcome for cider, after which the Republican committee congratulated itself for striking a blow for civil rights: “Glad the RTC has helped our community become more inclusive.”The culture wars were destined to spill someday into the rarefied precincts of Greenwich. But who in the name of George Bush would have expected the charge to be led by a band of Trump acolytes who have taken control of the town’s Republican committee?The electoral worth of the party’s far-right swerve will be tested nationwide in next week’s midterm elections. Here in Greenwich, long a bastion of moderate Republicans like the elder Mr. Bush — a Greenwich Country Day alum — the takeover has people asking: Who are these Greenwich Republicans? And did they lock the town’s traditional Republican leaders in the hold of some yacht in Greenwich Harbor?The answer: They are a small, well-organized group that essentially applied the “precinct strategy” espoused by the former Trump strategist Stephen K. Bannon, which calls for toppling local political establishments to clear the way for like-minded Republican candidates who will one day guide the country’s future.Beth MacGillivray, the chairwoman of the new Republican Town Committee, which stands by its “inclusion” moment, said the previous committee was too moderate and lackadaisical. She promised a “red wave coming in the midterm elections.”But some Greenwich Republicans worry that their party may venture so far right it will fall off the political cliff. For them, former President Donald J. Trump is the unpredictable uncle who could turn the family barbecue into a three-alarm fire. You don’t deny the relationship, but you don’t volunteer it either.This ambivalence was highlighted in 2019 — even before the committee’s rightward lurch — when Republicans became apoplectic over a sudden sprouting of campaign signs linking Mr. Trump with Fred Camillo, their candidate for the mayor-like position of first selectman. “Trump/Camillo,” the signs said. “Make Greenwich Great Again.”The signs turned out to be the satirical handiwork of Mark Kordick, a registered Democrat and Greenwich police captain with 31 years on the force. According to court records, Mr. Camillo texted a supporter: “He better pray I do not win because I would be the police commissioner and he will be gone.”A satirical sign linking a Republican politician, Fred Camillo, to former President Donald J. Trump.Leslie Yager/Greenwich Free PressMr. Camillo did win, and Mr. Kordick was fired. In suing the town and several officials, Mr. Kordick said that the signs were “to remind undecided voters and moderate Republicans unhappy with Trump that Camillo and Trump were members of the same party.”The lawsuit, like the midterm elections, is pending.‘Clowns’ Against ‘Outsiders’Greenwich, with its increasingly diverse population of 63,000, is no longer a Republican stronghold known for fiscal conservatism and social moderation. Just five years ago, the town had considerably more registered Republicans than Democrats; today, Democrats outnumber Republicans, while unaffiliated voters, including more than a few disaffected Republicans, outnumber both.The State of the 2022 Midterm ElectionsElection Day is Tuesday, Nov. 8.House Democrats: Several moderates elected in 2018 in conservative-leaning districts are at risk of being swept out. That could cost the Democrats their House majority.A Key Constituency: A caricature of the suburban female voter looms large in American politics. But in battleground regions, many voters don’t fit the stereotype.Crime: In the final stretch of the campaigns, politicians are vowing to crack down on crime. But the offices they are running for generally have little power to make a difference.Abortion: The fall of Roe v. Wade seemed to offer Democrats a way of energizing voters and holding ground. Now, many worry that focusing on abortion won’t be enough to carry them to victory.A central reason: the divisive Mr. Trump, who was trounced here by Hillary Clinton in the 2016 election. He was vilified by the town’s progressives and disliked by most moderate Republicans, though he found support among some wealthy and influential residents.It was against this backdrop that the Republican Town Committee chose Dan Quigley, 50, as its new chairman in early 2020. A financial services consultant, stay-at-home father and party moderate, he said he benefited from being a political neophyte: “No baggage. No animosity.”No such luck.Dan Quigley, the former chairman of the Greenwich Republican Town Committee, found himself at loggerheads with outspoken Trump supporters.Dave Sanders for The New York TimesBefore long, Mr. Quigley found himself at odds with Carl Higbie, a local Trump stalwart who, in 2018, had resigned his position with the Trump administration after CNN reported his history of offensive statements, including: “I believe wholeheartedly, wholeheartedly, that the Black race as a whole, not totally, is lazier than the white race, period.”Mr. Higbie, who said these past comments were either “flat-out stupid” or taken out of context, contacted Mr. Quigley about delivering Trump signs to party headquarters for the 2020 campaign, only to have Mr. Quigley explain that he had quietly prohibited Trump material, so as not to hurt the chances of the party’s local candidates. (Mr. Trump would be crushed here by Joseph R. Biden Jr., who would win 62 percent of the vote.)This irked Mr. Higbie, which led to internal bickering, which led to a compromise of sorts. Some Trump signs were delivered to party headquarters, only to be consigned to a corner and covered with a tarp.Mr. Higbie, 39, is now the host of a morning weekend program on the right-wing broadcaster Newsmax. He said recently that he had long been unhappy with the “very establishment Jeb Bush-style Republican Party” in his hometown — “historically squishy,” he said — and he was still annoyed by Mr. Quigley’s suppression of Trump signs.Carl Higbie, a Newsmax host and former member of the Trump administration, clashed with the committee’s leadership.Tyler Sizemore/Hearst Connecticut Media“Look, dude, if you’re not going to support our presidential nominee, the sitting president, we have a problem with that,” Mr. Higbie said. “It turned a lot of people off.”Mr. Quigley called the moment “the first altercation I had with this group.”It was not the last.Months later, some Republicans vehemently opposed one of the Town Committee’s nominees for the Board of Education: Michael-Joseph Mercanti-Anthony, a longtime educator with a doctorate in education leadership whose employment in the New York City school system made him suspect. What’s more, he had donated about $400 to the Biden campaign.“They saw that as unforgivable,” said Mr. Mercanti-Anthony, 47, who described himself as “a conservative who does not believe Trump possesses the competence to be president.”Mr. Higbie used his Newsmax platform to criticize Mr. Quigley and Mr. Mercanti-Anthony as Republicans in name only. He showed their photographs to his national audience, including one of Mr. Mercanti-Anthony with his two young sons — their faces blurred, Mr. Higbie said, “because we’re civil here.”“We can’t let these clowns get away with this anymore,” Mr. Higbie told his viewers.Mr. Mercanti-Anthony won more votes than any other school board candidate in last November’s local elections, part of a Republican sweep that included retaining control of the town’s powerful finance board. An unqualified success for Mr. Quigley, it would seem.Michael-Joseph Mercanti-Anthony was elected to the school board despite his opposition to Mr. Trump and being portrayed as a Republican in name only.Leslie Yager/Greenwich Free PressDays later, in an opinion piece in the local paper, Mr. Quigley urged Republicans to move on from Mr. Trump — an “ego-driven political opportunist,” he wrote — and described the party’s right wing as “angry outsiders” who base their conclusions “on dodgy facts and conspiracy theories.”Most Greenwich Republicans do not share their values, he wrote with confidenceOusting the Old GuardOrganizations like the Greenwich Republican Town Committee may seem more like vanity projects than vehicles of power. But they decide who appears on a party’s endorsed ballot for the school board, the town council, the state legislature — the steppingstones to higher office.Normally, the committee’s underpublicized meetings attract few people. But on two frigid nights in early January, hundreds of registered Republicans showed up for caucuses to elect their committee members for the next two years — after some stealthy coordination by an anti-moderate contingent that included sending out “Dear Neighbor” leaflets vowing to “protect Greenwich from turning into San Francisco.”The insurgent slate overwhelmed the Republican caucuses, winning 41 of the 63 committee seats.“A complete, total blood bath,” acknowledged Mr. Quigley, who commended the winners for being “well organized” but also accused them of a “political coup.”“It made no sense,” he said. “We weren’t Democrats, we weren’t socialists, but people who previously were not engaged in politics believed that narrative.”Five self-described working mothers took over the executive committee, including Mr. Quigley’s successor as chair, Ms. MacGillivray, 60, who was fairly new to politics. She later recalled that when asked in 2020 to help Kimberly Fiorello, a conservative Republican, run for state representative, she initially balked, joking, “It’s golf season, for God’s sake.”Ms. MacGillivray, more seasoned now, wrote in an email that despite the electoral success under Mr. Quigley, people were dissatisfied with his “inactions” and wanted a “more dynamic and responsive” leadership. Others said that dissatisfaction with the “woke” direction of the public schools also played a role.Beth MacGillivray, the committee chairwoman, attended a Greenwich Republican clambake in September with Senator Rick Scott of Florida, right.Dave Sanders for The New York TimesThe new committee cites the familiar guiding principles of limited government, parental rights and individual freedom, as well as “America First,” the catchall trope of Mr. Trump. Still, the abrupt change in tone has been like golf cleats clattering on a country club’s marbled floor.There was the perceived need to champion white inclusion in mostly white Greenwich, for example. And the time Ms. MacGillivray, in opposing transgender athletes in scholastic sports, told the school board that the men on her college ski team were consistently stronger and faster — and “even one of the male ski racers” who was “gay,” she said, “out-skied any girl or woman on the racecourse every time.”There is also the committee’s connection to the Greenwich Patriots, a hard-right group that at times seems like the id to the Town Committee’s ego. The Patriots contend that Covid-19 vaccines are unsafe, rail against “highly sexualized, pornographic and profanity-laced content” in schools, and serve as a conduit for Mr. Trump, promoting his events and sharing his specious claim that the 2020 election was stolen.“In case you are wondering,” the group’s daily newsletter once advised, “election fraud was rampant in the 2020 election in all 50 states, including in Connecticut.”False. More than 1.8 million Connecticut residents voted in the 2020 election, but the state’s Elections Enforcement Commission has received just 31 complaints alleging irregularities. Three resulted in fines, with the rest dismissed, pending or found inconclusive.A Different Kind of PlatformOne way that the Town Committee severed its moderate past was by declining to participate in the candidate debates sponsored by the League of Women Voters of Greenwich. The league’s local chapter was “clearly biased” and dominated by Democrats, Ms. MacGillivray said, with a tendency to take “strident, vocal positions on political issues” like voting rules.The chapter’s president, Sandy Waters, a former Republican member of the Greenwich school board, disputed every point. The nonpartisan organization’s not-for-profit status allows it to support policy issues such as early voting, she said, and the decision by Republicans not to participate hindered the pursuit of an informed electorate.Republican committee members spoke to voters outside Town Hall in August.Dave Sanders for The New York TimesCandidates around the country are increasingly sidestepping events like debates. But some critics said that by doing so, Greenwich Republicans had managed to avoid questions about Covid vaccinations, abortion rights, the Jan. 6 Capitol riot, false claims of electoral fraud — and Mr. Trump.Ms. MacGillivray said that the subject of Mr. Trump played no role in the caucuses. She also wondered why, in 2022, the media remained obsessed with the man.Perhaps because Mr. Trump’s ideology and style influence local politics so profoundly that John Breunig, editorial page editor of The Stamford Advocate and Greenwich Time, described Greenwich as a three-party town: Democrat, Republican and “Trumplican.”The Greenwich Republican ecosystem is such that James O’Keefe, the founder of the conservative activist group Project Veritas, is practically a local celebrity.In March, Mr. O’Keefe promoted his latest book at a gathering in a Greenwich hotel that was organized with the help of Jackie Homan, the founder of the Greenwich Patriots and an unsuccessful candidate on the caucus slate that ousted the moderate Quigley group.Months later, Project Veritas released hidden-camera video of a Greenwich elementary school vice principal boasting to an unseen woman that he tried to block the hiring of conservatives, Roman Catholics and people over 30. The circumstances behind the heavily edited video are unclear, and the vice principal, since suspended, did not make unilateral hiring decisions.Still, some Greenwich Republicans asserted that the video reflected a larger effort to “indoctrinate students with specific political ideologies.” This would include antiracism training and social emotional learning, which aims to nurture mental well-being, among other goals, but which some on the right believe is intended to make white children feel guilty for being white.Such positions have baffled more moderate Greenwich Republicans like Mike Basham, a former member of the first Bush administration who recently moved to South Carolina after many years as a prominent local leader of the party.“How can people that bright believe some of this stuff?” he asked. “Who indoctrinated them?”An Ex-President’s ShadowMr. Trump’s name doesn’t need to appear on campaign signs for him to have sway in Greenwich.For example, there is Ms. Fiorello, 47, the state representative, who is up for re-election. A participant in the effort to replace Mr. Quigley, she has moderated events with doctors accused of spreading misinformation about Covid, as well as with No Left Turn in Education, a group opposed to what it calls “the radical indoctrination and injection of political agendas” in schools.Kimberly Fiorello, a Republican state representative, helped to push out the local committee leadership.Dave Sanders for The New York TimesAfter the Federal Bureau of Investigation executed a search warrant at Mr. Trump’s Mar-a-Lago estate in Florida — collecting boxes of material, including highly classified documents, that he had failed to return to the government — Ms. Fiorello posted a video expressing concern over the “raid.”“We have to secure this republic,” she said. “Active and engaged citizens is what it takes. Peaceful protest. But citizens, we need to speak out and protect what this country is founded on. There are some things that are happening right now that are simply unacceptable and truly un-American.”There is also Leora Levy, a wealthy Greenwich Republican who, in supporting Jeb Bush for president in 2016, described Mr. Trump as “vulgar” and “ill mannered.” When Mr. Trump won the nomination, she set aside her concerns to become an enthusiastic supporter, and he later nominated her to be ambassador to Chile (the nomination never received Senate approval).When Ms. Levy, 65, decided to challenge the Democratic incumbent, Richard Blumenthal, for the Senate this year, the state Republican committee declined to endorse her. But her local Republican committee did, as did Mr. Trump, during a phone call shared at a crowded party function.Six days later, Ms. Levy won the primary.Leora Levy, a Trump-backed Greenwich Republican, is running to unseat Senator Richard Blumenthal, a Democrat.Dave Sanders for The New York TimesSince then, she has joined her Greenwich compatriots in trying to navigate the tricky Trump terrain.“I was honored to win his endorsement,” Ms. Levy told The CT Mirror, a nonprofit news organization. “He and I agree completely on policy, but I’m Leora Levy … Trump is not on the ballot. Leora Levy is.”Last month the Levy campaign held a fund-raising event at Mar-a-Lago that featured Mr. Trump. For $25,000, you could have your photograph taken with the man who lost Greenwich twice. More