In 2016, Arizona Republicans controlled both Senate seats and delivered a victory to Donald J. Trump. By 2020, they had lost each of those statewide elections, and Mr. Trump was one of only two Republican presidential candidates to lose the state in more than 50 years.

The losses are not prompting any sort of soul-searching in the state Republican Party.

Instead, when the party leadership meets this weekend, the most pressing items on the agenda will be censuring three moderate Republicans who remain widely popular in Arizona. The all-but-certain state party scolding will not have any practical impact, but the symbolism is stark: a slap on the wrist for Cindy McCain, the widow of the Senator John McCain; former Senator Jeff Flake and Gov. Doug Ducey.

While some Republicans nationwide are beginning to edge away from Trumpism, Arizona is a case of loyalists doubling down, potentially dividing the party in fundamental and irreparable ways. The consequences could be particularly acute in a state that had long been a safe Republican bet, but that has seen a significant political shift in recent years, in large part because of both the increased political participation of young Latinos and the changing views of white suburban women.

The state party chair, Kelli Ward, who was first elected in 2019, announced that she would run for re-election only after speaking to Mr. Trump, who she said enthusiastically encouraged her. For months, Ms. Ward has sent out fund-raising appeals talking about what she calls the “stolen” election. Arizona’s state legislators have been frequent fixtures at “Stop the Steal” rallies in the state, pushing conspiracy theories and debunked fraud accusations. Two congressmen from the state helped plan the Jan. 6 rally in Washington which drew the mob that later stormed the Capitol. They have also written supportive statements about the rioters.

When Ali Alexander, a primary organizer of the Capitol protest, wrote on Twitter “I am willing to give up my life for this fight,” the Arizona Republican Party account retweeted and asked its followers: “He is. Are you?”

The far-right extremism is hardly new in Arizona. The state gave birth to anti-immigrant border militias, legislation that effectively legalized racial profiling, and is home to Joe Arpaio, the former sheriff of Maricopa County who pushed a hard-line message on immigration. But the kind of Trump fervor that has been on vivid display in the state since the November election has taken on momentum that even some conservatives in the state find alarming. Within hours of Joseph R. Biden Jr. being declared the winner of the election, hundreds of protesters showed up at the State Capitol, many slinging military-style weapons and waving flags portraying Mr. Trump as Rambo.

The Arizona Republican Party has long engaged with and promoted extremist elements, particularly on immigration, and has an anti-government streak that stretches back to Barry Goldwater, a former senator of the state. Still, some Republicans in Arizona have now begun to sound the alarm, warning that the party is pushing itself into oblivion in a state where independent voters make up nearly a third of the electorate.

“The angry, spiteful messaging that is coming out of the party right now, it’s not going to win the new west,” said Adam Kwasman, a former state legislator who was once named one of the most conservative lawmakers in the state while in office and who voted for Mr. Trump last year.

He said his loyalty was to the party more than to the president. “If we want Arizona to not become Colorado, to just hand this state to the Democrats, we have to be laser-focused on working families, and if we don’t do that, we’re doomed,” he said, adding, “We’re in a real disconcerting place.”

Already, there are hints that Mr. Kwasman is right to worry. Nearly 5,000 registered voters dropped their Republican Party affiliation in the week after Jan. 6. Some former Republican operatives warn that a steady erosion of the party’s narrow edge in voter registration is coming.

“There’s an act of serial larceny going on right now,” said Chuck Coughlin, a longtime Republican strategist in Phoenix who changed his own party affiliation in 2017 and is now an independent. In the dozens of calls Mr. Coughlin has received from worried Republicans, he said, his advice has been consistent: Don’t bother trying to save anyone who has supported “acts of sedition.” “It has become a party of outright contempt for any authority except for one man. The Republican Party is in the midst of its own French Revolution now.”

It is difficult to know just how much the state party leadership represents the core rank-and-file Republicans. But thousands of voters have shown up at the State Capitol in Phoenix for several “Stop the Steal” rallies, including an impromptu protest the day the general election was called in November. Like other state capitols around the country, the copper-domed building in Phoenix was surrounded by a six-foot high wire fence over the weekend, and law enforcement remains on high alert for potential violence on Inauguration Day.

A group of Republican state lawmakers have issued a subpoena to the Maricopa County board of supervisors, demanding that it turn over ballot counting machines, along with images of all mail-in ballots and detailed voter information. Though Democrats won statewide, Republicans maintained their control of both houses of the Legislature, enabling them to continue to litigate the debunked notion of fraud despite the fact that all eight legal challenges failed in court.

“We kept our majority and that’s more cause for suspicion of a fraudulent election,” said Sonny Borrelli, a state senator, falsely suggesting that the presidential ballots had been tampered with. Mr. Borrelli said he had received more than 100,000 messages from residents in Arizona urging the Legislature to further investigate claims of fraud. “It just adds fuel to the fire, and we’re going to keep focus on that fire,” he said. “That’s our job.”

A statewide test for the party is not far-off: Mark Kelly, the Democrat who won a special election for his Senate seat in November, will be up for re-election in 2022. Mr. Ducey is widely discussed as a possible challenger, running as a business-friendly moderate. But Republicans across the spectrum say that although Mr. Ducey was the last Republican to win a statewide election, he would face an uphill battle during a Republican primary.

“It would be a bare-knuckled brawl, and it would probably be nasty,” Mr. Coughlin said.

Mr. Ducey and his aides declined to comment for this article, and he is not expected to challenge the state party’s vote to censure him.

Any accusations of nastiness do not appear to deter the state party or Ms. Ward, who did not return calls seeking comment. Last month, Ms. Ward tweeted at Mr. Ducey with the hashtag #STHU — internet speak for “shut the hell up” — when Mr. Ducey defended the state’s election process.

Mr. Ducey responded by saying that the feeling was mutual and that Ms. Ward should “practice what you preach.”

And this is not the first time the state party has gotten into a public flap with the McCain family. In 2014, the party censured Mr. McCain himself over his voting record.

Ms. McCain has responded to the threat of her own censure with equal parts annoyance and amusement.

“It’s about doing what’s right for the country,” Ms. McCain said during an appearance on “The View,” which is co-hosted by her daughter Meghan. “Certainly, Senator Flake and our governor have made some very tough decisions lately and in the past, but it was for the good of our state and our country.”

“You know, I’m in good company,” she added. “I think I’m going to make T-shirts for everyone and wear them.”

Mr. Flake, who endorsed Mr. Biden in the presidential election, wrote on Twitter that he, too, was unconcerned with the censure.

“If condoning the President’s behavior is required to stay in the Party’s good graces, I’m just fine being on the outs,” he wrote.

Robert Graham, who served as chairman of the state party from 2013 to 2017, called the censures a waste of time at best, and pointed out that Mr. McCain won each of the statewide elections he ran.

“The only objective of a state party is to win elections,” Mr. Graham said. “When the state chairman attacks somebody in his family, you fracture the party. The resolution will pass, it will disenfranchise a bunch of Republicans and it will be put in a folder and become memorabilia forever.”

Rather than further fracturing the base, Mr. Graham said, party officials should be focused on solidarity.

“The right has become even more emboldened because they had someone in the highest office with a giant megaphone,” he said. “But in Arizona you have a governor who is in his last term, so it’s time for the Republican Party to rally, pull together and morph to what it is going to be for the next four years. The mission here is supposed to be if you take a beating, make a transformational refresh.”

John Fillmore, a state representative who has attended several protests, likened the debate within the party to a “cleansing,” and said he was more concerned about purging those who have criticized Mr. Trump than losing voters.

“The party is discombobulated and the absolute turncoats like Jeff Flake and Liz Cheney will feel the wrath of the Republican voters,” Mr. Fillmore said. “We’re a family, and ultimately what happened was that members of the family went against the family and they did it with a vengeance. It’s what The Godfather said: Don’t ever go against the family. It’s sad.”

On Jan. 6 in Phoenix, a group of protesters objecting to the certification of the presidential election results erected a guillotine near the gold-domed Capitol. The group passed out a document to reporters explaining its actions: Concerned Americans, they said, were worried that votes had not been counted properly. They had “gathered peacefully, made phone calls and begged their elected officials to listen to their concerns.”

As they gathered, the mob in Washington breached the nation’s Capitol building — actions the Arizona party would later blame on antifa.

On Sunday, in Phoenix and in capitals around the country, law enforcement was bracing for another round of protest. Only a handful of protesters showed up. The guillotine was gone.