PHILADELPHIA — Hillary Clinton’s embrace of gay Americans at the Democratic National Convention failed to win over at least one transgender delegate in the crowd.

California delegate Mia “Tu Much” Satya said she had many misgivings about Mrs. Clinton, including her hawkish foreign policy, but mostly she felt the former first lady, senator and secretary of state was a fair-weather friend of the lesbian, gay, bisexual and transgender community.

“It’s entirely possible that she supports LGBT people, but it sure took a long time,” said Ms. Satya, who supported Sen. Bernard Sanders, a self-identified democratic socialist, in the primary.

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Ms. Satya, who works as a comedian, model and emcee in San Francisco, said that Mrs. Clinton only supported gay issues such as same-sex marriage when it became “political suicide” to remain in opposition.

“I’m anti-war. Economic justice and world peace are LGBT issues, and she hasn’t done well on world peace,” she said.

She added that she wouldn’t vote for Republican presidential nominee Donald Trump, who has sought to make inroads with gay voters, saying that she would consider other options in November.

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Mrs. Clinton was slow to favor same-sex marriage. She reversed from opposition to support just within the past couple of years, as the gay-marriage cases wound through the court system in preparation for the expected Supreme Court ruling on state laws defining marriage as the union of a man and a woman.

She also has had to seek forgiveness for supporting the anti-gay military policy of “don’t ask, don’t tell” that was instituted by her husband, President Bill Clinton, and ultimately repealed by President Obama to allow openly gay service members.

She has tried to put all that behind her campaign.

The resistance to Mrs. Clinton confounded her LGBT voters from the convention stage in Wells Fargo Center. Speaker after speaker gave a shout out to gay rights and record number of LGBT delegates filled the arena.

“Before I came out to the world on the cover of Sports Illustrated, I came out privately to the Clinton family,” said Jason Collins, who was the first openly gay NBA player. “I knew they would accept me for who I was.”

The speaker lineup includes the first transgender person to take the stage at a major party convention. LGBT activist Sarah McBride, who made national headlines coming out as transgender while student body president at American University, will address the convention Thursday.

Mrs. Clinton also named Marisa Richmond, a Democratic activist from Nashville, Tennessee, as the convention’s official timekeeper, making her the first transgender person to be a podium official for a major party.

The moves countered Mr. Trump’s pledged to make gay rights part of his national security agenda after a Islamic State-inspired gunman attacked a gay nightclub in Orlando, Florida, killing 49 people in the worst terror attack in the U.S. since 9/11.

He repeated his pledge to be the defender of the gay community in his acceptance speech last week at the Republican National Convention in Cleveland.

“As your president, I will do everything in my power to protect our LGBTQ citizens from the violence and oppression of a hateful foreign ideology. Believe me,” Mr. Trump said to a burst of applause.

He then went off script and said: “I have to say, as a Republican, it is so nice to hear you cheering for what I just said.”

The remark won him kudos but many LGBT activists remained skeptical of the Republican nominee.

Mrs. Clinton also has allied herself with opponents of the North Carolina law requiring people to use public restrooms based on their biological sex, which caused a firestorm of protests that included major businesses, entertainers and sports events boycotting the state.

During the primary race, Mr. Trump voiced opposition to the bathroom law. He said it was bad for business but then, under pressure from conservatives, took the position that it was an issue that states should decide.

Convention delegate Chris Sgro, the only openly gay member of the North Carolina Legislature and a prominent opponent of the bathroom law, said his community was “very solidly” for Mrs. Clinton.

“Absolutely we are standing with Hillary Clinton like our rights depended on it — because they do,” said Mr. Sgro, adding that he completely disagreed with critics who say her support for gay rights is a political calculation.

“I don’t think it is pandering at all. She has fought for civil rights and empowerment for a long time,” he said, adding that supporting Mr. Trump was out of the question.

“He is dangerous, homophobic and misogynistic and would be dangerous for our community,” he said.