For almost 40 years, a stretch of Manhattan’s West Side from Greenwich Village to Hell’s Kitchen has had a gay representative in the City Council, reflecting the district’s large L.G.B.T.Q. population and its role in history as the site of the Stonewall riots, a pivotal moment in the gay and transgender rights movement.

But a special election next Tuesday may see a straight person elevated to the Council seat for the first time in decades, after Mayor Zohran Mamdani endorsed Lindsey Boylan, an activist who was also the first woman to accuse former Gov. Andrew M. Cuomo of sexual harassment.

Mr. Mamdani’s endorsement has injected questions of ideology and identity into a contest that previously attracted little attention and raised questions about how important it is to the voters in the Council’s Third District, and to the city at large, to elect an L.G.B.T.Q. person to the seat.

It has also drawn the race into a broader conflict between Mr. Mamdani and Julie Menin, the Council speaker and a more moderate Democrat. Ms. Menin has endorsed Carl Wilson, a community activist and legislative aide who is gay.

Mr. Mamdani’s endorsement came just before the start of early voting and quickly elevated Ms. Boylan, a democratic socialist, in a contest that had previously been dominated by Mr. Wilson, who had secured a wide range of endorsements and said he planned to join the Council’s progressive caucus if elected.

The mayor’s decision to wade into the race has upset some gay activists, including Allen Roskoff, 76, who successfully pushed to create what he called a “gay winnable” Council seat in 1991.

“We want to continue honoring the people before us who did give their blood, sweat and tears to acquire this seat,” said Mr. Roskoff, whose late partner, Jim Owles, was a prominent activist who ran unsuccessfully for City Council in the area in 1973.

Mr. Roskoff has endorsed Mr. Wilson, but says he would not have done so if he did not believe him to be the best candidate.

“In this district we have someone eminently qualified, and our history needs to be respected,” Mr. Roskoff said. He added: “I don’t think a straight person can say, ‘I would represent you just as well.’ No. That’s not what representation is.”

Others, including Mr. Wilson himself, have pushed back, saying the focus should be on the candidates’ proposals and experience and not their sexual orientation.

“There have been wonderful queer people elected from the district over the last 30-some years,” said Cynthia Nixon, the actress and activist, who supports Ms. Boylan. “But I feel now and have always felt we should be voting for people not based on their identity, but based on who they are.”

Some have called the idea of a “gay seat” on the City Council reductive and patronizing to voters, especially in a city that now has many L.G.B.T.Q. elected officials.

“Hell’s Kitchen is an inclusive neighborhood of everybody — every race, every sexuality, every religion,” said Marisa Redanty, a community activist in that neighborhood.

Mr. Wilson and Ms. Boylan are competing to finish Erik Bottcher’s term, which lasts through December. Mr. Bottcher vacated his seat earlier this year when he was elected to the State Senate. The winner is expected to compete in the Democratic primary in June and the general election in November to serve a full term on the Council.

Two other heterosexual candidates, Leslie Boghosian Murphy and Layla Law-Gisiko, are also running but are considered long shots.

In an interview, Mr. Wilson said that while he thought it was “not a requirement” that the district be represented by an L.G.B.T.Q. person, “it’s an important perspective.”

“I am way more than just a gay candidate — way more,” said Mr. Wilson, who has deep relationships in the district and has worked as Mr. Bottcher’s chief of staff. “I’m also the candidate with the longest track record of on-the-ground service in this district and the experience to deliver from Day 1.”

Mr. Wilson and his supporters marked the first day of early voting last weekend with a “drag out the vote” event on Ninth Avenue, where local drag queens urged people to vote. Days later, he and Ms. Boylan both appeared in the West Village to commemorate the 60th anniversary of an important protest held at Julius’, a historic gay bar.

Ms. Boylan has responded to the debate over L.G.B.T.Q. representation delicately. In an interview, she said she would never “take away or diminish how anyone feels” about the prospect of replacing a gay council member with a straight one.

She has also pointed out that many issues, including affordability, affect people of all sexual orientations, especially in a district that includes some of the most expensive neighborhoods in the United States.

“About half of our residents are severely rent-burdened,” said Ms. Boylan. “It’s a real challenge to stay here.”

Ms. Nixon echoed that point, saying the Third District used to be “a much scrappier part of the city.”

“And a lot of those queer people have been priced out,” she added.

The mayor’s endorsement of Ms. Boylan came at a time when he needs allies on the Council. Mr. Mamdani and Ms. Menin have been engaged in a feud over a range of issues, including taxation and the budget.

When he endorsed Ms. Boylan, Mr. Mamdani praised her as a leader who shared his vision of New York’s future, and noted her courage in speaking out against the former governor.

“As we work to usher in a new era in our city’s politics and advance our affordability agenda,” Mr. Mamdani said, “I need partners in the work like Lindsey.”

A spokesman for the mayor, responding to controversy over the endorsement, said in a statement on Thursday that Mr. Mamdani’s “commitment to the L.G.B.T.Q.I.A.+ community is clear, as is his record on the issue: establishing the first Mayor’s Office of L.G.B.T.Q.I.A.+ Affairs, naming director Taylor Brown as the first and highest-ranking transgender leader in the history of the city’s government and supporting numerous queer candidates over the years.”

Ms. Menin is very invested in the outcome of the race and has begun soliciting funds for Mr. Wilson’s campaign, according to someone familiar with the outreach.

Before Mr. Mamdani made his endorsement, Mr. Wilson had secured the backing of influential local political clubs and labor unions, as well as elected officials including Representative Jerrold Nadler, whose district overlaps with the Council district, and the city comptroller, Mark Levine.

He has also received the backing of outside groups headed by influential Democrats, including Greg Goldner, the campaign manager for Mr. Cuomo’s mayoral bid.

Representative Nydia Velázquez, who represents parts of Brooklyn and Queens and has been in her own conflict with Mr. Mamdani over who should succeed her when she retires at the end of her term, has backed Mr. Wilson.

A former actor who lives in a walk-up rental on 10th Avenue, Mr. Wilson helped start a political club in the district, the Hell’s Kitchen Democrats, and served on the local community board before going to work for Mr. Bottcher.

Ms. Boylan rose to prominence as the first of a number of women to accuse Mr. Cuomo of sexual harassment, allegations he has denied but that nevertheless led to his resignation in 2021.

Since then, she has run unsuccessfully for Congress in 2020 and Manhattan borough president in 2021. She campaigned for Mr. Mamdani last year and joined the Democratic Socialists of America after he won the Democratic mayoral primary.

Mr. Mamdani defeated Mr. Cuomo in both that race and the general election last November. The mayor’s decision to endorse Ms. Boylan is widely seen as suggesting some lingering animosity toward Mr. Cuomo.

The debate over the district has highlighted the vast changes in New York and across the country since the election in 1991, when the place of L.G.B.T.Q. people in society was different.

Outspoken homophobia was widespread, there was little public understanding that transgender people existed, and the AIDS crisis was at its peak, with more than 30,000 New Yorkers dying of the disease in 1991 alone.

Today, there are many elected L.G.B.T.Q. officials in New York, including Representative Ritchie Torres, who represents parts of the Bronx in Congress, and Brad Hoylman-Sigal, the Manhattan borough president.

The City Council has several L.G.B.T.Q. members, including one gay Republican and gay Democrats from districts once seen as unwinnable for gay candidates.

Chi Ossé, 28, the co-chairman of the Council’s L.G.B.T.Q. caucus and ally of Mr. Mamdani’s, said he thought the debate over gay and transgender representation extended far beyond the Third District now.

For example, he said, he did not think a gay candidate could have won in his Brooklyn district 40 years ago.

“Decades ago, this was one of the only seats, if not the only seat, where a gay candidate could run and win,” he said. “But that has certainly changed.”

Rabbi Sharon Kleinbaum, the rabbi emeritus of Congregation Beit Simchat Torah, an L.G.B.T.Q. synagogue in Chelsea, has worked closely with each of the district’s council members since the early 1990s.

She said it was “really thrilling” when Tom Duane became the first gay candidate elected to represent the area in 1991. A vocal supporter of both Mr. Mamdani and Ms. Menin, she has endorsed Mr. Wilson.

“I think now it is less important whether or not Carl is gay than the values and perspectives he has,” Rabbi Kleinbaum said. “I think it’s great that he’s gay. I think we need to have that as part of the mix, but it’s not the only issue.”

Sally Goldenberg contributed reporting.