Donald Trump and possible rivals, like Gov. Ron DeSantis, are making appeals to conservative voters on race and gender issues, but such messages had a mixed record in November’s midterm elections.With a presidential primary starting to stir, Republicans are returning with force to the education debates that mobilized their staunchest voters during the pandemic and set off a wave of conservative activism around how schools teach about racism in American history and tolerate gender fluidity.The messaging casts Republicans as defenders of parents who feel that schools have run amok with “wokeness.” Its loudest champion has been Gov. Ron DeSantis, who last week scored an apparent victory attacking the College Board’s curriculum on African American studies. Former President Donald J. Trump has sought to catch up with even hotter language, recently threatening “severe consequences” for educators who “suggest to a child that they could be trapped in the wrong body.”Nikki Haley, a former South Carolina governor, who has used Twitter to preview her planned presidential campaign announcement this month, recently tweeted “CRT is un-American,” referring to critical race theory.Yet, in its appeal to voters, culture-war messaging concerning education has a decidedly mixed track record. While some Republicans believe that the issue can win over independents, especially suburban women, the 2022 midterms showed that attacks on school curriculums — specifically on critical race theory and so-called gender ideology — largely were a dud in the general election.While Mr. DeSantis won re-election handily, many other Republican candidates for governor who raised attacks on schools — against drag queen story hours, for example, or books that examine white privilege — went down in defeat, including in Kansas, Michigan, Arizona and Wisconsin.Democratic strategists, pointing to the midterm results and to polling, said voters viewed cultural issues in education as far less important than school funding, teacher shortages and school safety.Even the Republican National Committee advised candidates last year to appeal to swing voters by speaking broadly about parental control and quality schools, not critical race theory, the idea that racism is baked into American institutions.Still, Mr. Trump, the only declared Republican presidential candidate so far, and potential rivals, are putting cultural fights at the center of their education agendas. Strategists say the push is motivated by evidence that the issues have the power to elicit strong emotions in parents and at least some potential to cut across partisan lines.In Virginia, Gov. Glenn Youngkin’s victory in 2021 on a “parents’ rights” platform awakened Republicans to the political potency of education with swing voters. Mr. Youngkin, who remains popular in his state, began an investigation last month of whether Virginia high schools delayed telling some students that they had earned merit awards, which he has called “a maniacal focus” on equal outcomes.Mr. DeSantis, too, has framed his opposition to progressive values as an attempt to give parents control over what their children are taught.The Run-Up to the 2024 ElectionThe jockeying for the next presidential race is already underway.Taking Aim at Trump: The Koch brothers’ donor network is preparing to get involved in the Republican primaries, with the aim of turning “the page on the past” — a thinly veiled rebuke of Donald J. Trump.Trump’s Support: Is Mr. Trump the front-runner to win the Republican nomination? Or is he an underdog against Ron DeSantis? The polls are divided, but higher-quality surveys point to an answer.Falling in Line: With the vulnerabilities of Mr. Trump’s campaign becoming evident, the bickering among Democrats about President Biden’s potential bid for re-election has subsided.Democrats’ Primary Calendar: Upending decades of political tradition, members of the Democratic National Committee voted to approve a sweeping overhaul of the party’s primary process.Last year, he signed the Parental Rights in Education Act, banning instruction on sexual orientation and gender identity in early elementary grades.Democrats decried that and other education policies from the governor as censorship and as attacks on the civil rights of gay and transgender people. Critics called the Florida law “Don’t Say Gay.”Polling has shown strong support for a ban on L.G.B.T.Q. topics in elementary school. In a New York Times/Siena College poll last year, 70 percent of registered voters nationally opposed instruction on sexual orientation and gender identity in elementary grades.“The culture war issues are most potent among Republican primary voters, but that doesn’t mean that an education message can’t be effective with independent voters or the electorate as a whole,” said Whit Ayres, a Republican pollster, who worked for Mr. DeSantis during his first governor’s race in 2018.Gov. Glenn Youngkin made education during the pandemic a key part of his winning platform in blue Virginia.Kenny Holston for The New York TimesMr. DeSantis’s approach to education is a far stretch from traditional issues that Republicans used to line up behind, such as charter schools and merit pay for teachers who raise test scores. But it has had an impact.Last week, the College Board purged its Advanced Placement course on African American Studies after the DeSantis administration banned a pilot version, citing readings on queer theory and reparations for slavery. The College Board said the changes were not a bow to political pressure, and had been decided in December.Mr. DeSantis next rolled out an initiative to end diversity and equity programs in universities, to require courses in Western civilization and to weaken professors’ tenure protections.Mr. DeSantis’s communications staff did not respond to a request for comment.The current era of Republican culture-driven attacks on education began in 2020 during the pandemic with a tandem crusade against mask mandates in schools and the supposed influence of critical race theory.Yet, the political power of opposition to the critical race theory — which became a grab bag for conservative complaints about the teaching of American history and racial inequality — largely petered out by last year’s midterm general elections. A September polling memo by the Republican National Committee warned candidates that “focusing on C.R.T. and masks excites the G.O.P. base, but parental rights and quality education drive independents.”Of $9.3 million spent on campaign ads that mentioned critical race theory in 2022, in nearly 50 races for House, Senate and governor, almost all was spent during the primaries, according to an analysis by AdImpact. The issue was raised in only eight general election ads. The theme of “parents’ rights,” invoked in ads worth $9.8 million in 19 races, proved a more popular general election topic; it was used in 14 of those races.Conservative groups in 2022 also supported hundreds of candidates in local school board races with limited success. In nearly 1,800 races nationwide, conservative school board candidates who opposed discussions of race or gender in classrooms, or who opposed pandemic responses such as mask requirements, won just 30 percent of races, according to Ballotpedia, a site that tracks U.S. elections.“The Republicans do a great job of creating issues that aren’t issues,” said John Anzalone, a Democratic pollster who has worked for President Biden. He predicted that, in 2024, education issues that are now being raised by potential Republican presidential candidates would figure in the primary but would turn off voters in the general election.“The big lesson of 2022 is that Republicans didn’t have an economic agenda,” Mr. Anzalone said. “All they talked about was incredibly extreme positions, like on abortion and guns. Will they also talk about only extreme positions on these other things?”Kristin Davison, a political adviser to Mr. Youngkin, said that his 2021 campaign in blue Virginia was successful in part because it delivered nuanced and tailored messages on education. The campaign micro-targeted messages to each segment, including voters most interested in school choice, those opposed to critical race theory and those concerned about safety, she said.The strategy aimed to reverse Democrats’ historical advantage on which party voters trust on education.“Governor Youngkin started a movement in Virginia, standing with parents and going on offense on education,” she said.Republicans point to a May 2022 survey for the American Federation of Teachers union showing that voters in battleground states had slightly more confidence in Republicans than in Democrats, 39 percent to 38 percent, to handle education issues.Geoff Garin, whose firm, Hart Research, conducted that poll, said later surveys showed that Democrats had regained the advantage on education, a gain he attributed to Republicans’ focus on race being out of sync with parents.In a December survey by Hart for the teachers’ union, voters who were asked for the most important problems facing schools ranked teacher shortages and inadequate funding at the top. Critical race theory and “students being shamed over issues of race and racism” were near the bottom.“In addition to focusing on things that voters see as the wrong priorities, I expect that Republicans will deepen their problems with suburban voters by identifying so closely with book banning and whitewashing the treatment of race in schools and society,” Mr. Garin said.As Mr. DeSantis rolled out his latest plans last week to push Florida public universities to the right, he called universities’ diversity statements akin to “making people take a political oath.”Mr. DeSantis is believed to be weighing a presidential bid, but so far Donald Trump is the only declared candidate.USA TODAY NETWORK via Reuters ConnectDays earlier, Mr. Trump presented an education agenda of his own in a scripted 4-minute, 33-second video. It attacked many of the same targets that have made Mr. DeSantis both an intensely disliked figure to national Democrats and a star of Republicans, many of them once Trump supporters.After spending the past two years focused on the lie of a stolen 2020 election, Mr. Trump is playing catch-up, starting with education proposals.In his video, the former president called to cut school funding for critical race theory as well as “inappropriate racial, sexual or political content.”He also proposed measures that seemed to echo those of Mr. Youngkin, including putting “parents back in charge” and investigating school districts for “race-based discrimination,” singling out “discrimination against Asian Americans.”Francis Rooney, a former Republican congressman from Florida and a Trump critic, said that the former president’s education proposals were an effort to become relevant on issues that drive conservative voters.“I think he’s becoming Mr. Me-Too,” he said of the former president. More