When President George W. Bush needed to shore up support with social conservatives during his re-election run in 2004, he turned to a familiar political tactic: demonizing L.G.B.T.Q. rights. On the campaign trail and from the White House, the Republican leader began championing a constitutional amendment banning same-sex marriage, praising unions between a man and woman as “critical to the well-being of families.”

Sixteen years later, when another issue of L.G.B.T.Q. rights popped up in the midst of another presidential campaign, the Republican incumbent responded with little more than a shrug.

“They ruled and we live with their decision,” President Trump told reporters after the Supreme Court issued a decision on Monday protecting the rights of L.G.B.T.Q. workers. “That’s what it’s all about. We live with the decision of the Supreme Court.”

For decades, most Republican leaders have opposed L.G.B.T.Q. civil and marriage rights, views that remain embedded in the party’s platform and its activist base. Last weekend, party activists in Virginia punished Representative Denver Riggleman, a first-term Republican, for officiating a same-sex marriage ceremony; they chose a self-described “biblical conservative” as their G.O.P. nominee for November. And the Trump administration continues to limit civil rights protections for transgender people and bar most of them from military service.

Yet today, widespread battles over L.G.B.T.Q. rights are less frequent among parts of the Republican Party — not just among some corporate leaders and political donors who dislike openly bigoted fights, but also among many of the rank-and-file Republicans who say in polling that they support at least some rights and protections for L.G.B.T.Q. people

Last year, according to Pew, roughly three in five Americans said they supported same-sex marriage — up from half that share in 2004. Among Republicans and Republican-leaning independents, 44 percent supported same-sex marriage last year, up from 19 percent. Wide majorities of the country also support extending workplace protections to L.G.B.T.Q. Americans, according to surveys taken before the Supreme Court’s ruling.

The consensus was so broad that last year, even among white Republican men over age 50 holding favorable views of Mr. Trump, 52 percent said that workplace protections and other nondiscrimination laws should apply to L.G.B.T.Q. people, according to a Public Religion Research Institute poll.

“On L.G.B.T. rights, everyone has moved on this issue,” Robert Jones, the founder of PRRI, said in an interview, referring to voters across the political spectrum. “Whether you’re talking about marriage equality, nondiscrimination protection — everybody has moved. Seniors have moved, white evangelicals have moved, base Republicans have moved.”

In interviews this week, several Republican voters in battleground states reacted to the Supreme Court ruling by expressing support broadly for civil rights for L.G.B.T.Q. people. Some were gently critical of Mr. Trump on points, while others said the most unexpected thing about the decision was that two Republican-nominated members of the court, Chief Justice John G. Roberts Jr. and Justice Neil M. Gorsuch, joined the court’s four more liberal justices on the majority opinion, which Justice Gorsuch wrote.

“As conservatives, they usually go by the rule of law, so I was surprised,” said Wayne Bradley, 43, a Republican from Detroit. “But I’m comfortable with the decision they made. Everyone deserves respect and with all the other things that are going on in the world, maybe that played a part in their decision. Everybody deserves protection.”

Margie Dougherty, 61, a Republican and Trump backer from Bayside in suburban Milwaukee, said she believed the president was not taking the right approach with his restrictions on transgender people serving in the military.

“If a person can perform the duties of a job or role they are hired and trained for, then they should be allowed to do the job,” she said.

For many transgender and nonbinary Americans, however, changes in public opinion can be cold comfort given that prejudice and hate crimes remain a harsh reality in their lives. In interviews, some expressed concern that the new Supreme Court ruling could take the focus away from work that still needs to be done.

“The big picture is that employment is only one of many places where gay trans people are discriminated against,” said Patrick Cognato, an English major at Binghamton University who is nonbinary. “Things like health care, housing and education are really important, too, and have a serious effect on people’s everyday lives. People can’t wait for these to be addressed because it affects them every day.”

Last year, in a separate PRRI survey, 62 percent of Americans said that in recent years they had become more supportive of transgender rights, not less. Even a slim majority of white evangelicals — a Republican bastion — said they had grown more supportive.

But it was only five years ago that transgender Americans became a political target of Republicans trying to regulate the use of public bathrooms. Some political observers believe that the Republican focus on the issue backfired — particularly when a Democrat, Roy Cooper, won the governor’s race in North Carolina after the state’s “bathroom bill” became a flash point in the campaign. That legislation required transgender people in government and public buildings to use the bathroom that corresponds with the gender on their birth certificate.

The law drew nationwide outrage, prompting companies to cancel planned expansions and move events out of the state, costing North Carolina jobs and tax revenue. Last year, the law was partially repealed by a federal judge.

Whatever the change in attitudes, however, transgender Americans remain heavily targeted for hate crimes, violence and discrimination. Black transgender people suffer disproportionate levels of police violence, and the American Medical Association said last fall that killings of transgender people, especially women of color, amounted to an epidemic.

If some Republicans have grown more accepting of L.G.B.T.Q. rights, Mr. Trump, his administration and the party leadership appear out of step with those parts of the base.

“I cannot think of another administration that has gone out of its way to discriminate against transgender people specifically,” said Gabriel Arkles, a senior staff lawyer for the American Civil Liberties Union working on L.G.B.T.Q. rights. “There are other administrations that were terrible for transgender people — the Reagan administration’s management of the H.I.V. epidemic, Clinton’s welfare and prison reform — but these weren’t situations where they were specifically naming transgender people in their policies.”

On other issues, Mr. Trump called same-sex marriage “settled law” shortly after taking office, but he also promised to “seriously consider” a Supreme Court justice who would once again outlaw the constitutional right. Congressional Republicans and Mr. Trump continue to resist the Equality Act, Democratic-sponsored legislation that would extend anti-discrimination rules for L.G.B.T.Q. Americans. And the executive committee of the Republican National Committee decided this month to carry over the 2016 party platform, which calls for a constitutional amendment overturning the 2015 Supreme Court decision that struck down laws defining marriage between one man and one woman.

With the president’s re-election prospects looking precarious at the moment, both Mr. Trump and some party leaders appear wary of antagonizing the loyal voters and activists in the most conservative parts of his base. Yet even some leaders on the right say that opposition to L.G.B.T.Q. protections doesn’t carry the same political potency that it once did in some of the most conservative quarters of the party.

“Religious freedom and the protection of unborn lift ranks far higher in the hierarchy of the concerns from faith-based voters,” said Ralph Reed, the chairman of the Faith and Freedom Coalition, which works to drive evangelical voters to the polls.

On the campaign trail, most Republican elected officials now generally avoid broadcasting their opposition to same-sex marriage, except in select primary campaigns in deeply conservative districts. Meanwhile, a record number of L.G.B.T.Q. candidates won seats in the 2018 midterms, with 161 openly lesbian, gay, bisexual and transgender people elected, according to the Victory Fund, a nonpartisan political action committee devoted to electing L.G.B.T.Q. candidates. Most were Democrats.

Ed Goeas, a Republican pollster, said that what was once a hot-button issue for voters on the right had turned into something of a nonstarter.

“There was a period of concern over where things were moving on gay marriage: that a church that refused to marry a gay couple could be sued,” Mr. Goeas said in an interview. “The fact of the matter is, nothing’s really pushed it to that extent, everything’s sort of settled down into normalcy, and I don’t sense that it’s a big issue today.”

Even as national attitudes have evolved on questions around gender and sexuality, analysts said that the Republican Party under Mr. Trump has hardly let go of cultural issues altogether. It has simply shifted toward talking more about immigration and race, including in his attacks on protesters, immigrants and black celebrities.

“The new culture war is not abortion or same-sex marriage, the new culture war is about preserving a white, Christian America,” said Dr. Jones, the PRRI pollster. A 2019 poll from his organization found that, even as many Americans’ views on race had moved to the left in recent years, 69 percent of Republicans said they believed that discrimination against white people was just as much of a problem as discrimination against racial minorities.

“That’s what Trump’s really leading with,” Dr. Jones added. “The ‘Make America Great Again’ thing — the way that was heard by most white evangelical Protestants, white working-class folks, was saying: ‘I’m going to preserve the composition of the country.’”

Lisa Lerer reported from Washington, and Giovanni Russonello and Isabella Grullón Paz from New York. David Umhoefer contributed reporting from Milwaukee, and Kathleen Gray from Detroit.