The church still opposes same-sex marriage, and advocates say Mormon bishops still regularly excommunicate openly gay members in some more conservative congregations. Church leaders say that being gay is not itself a sin, but it urges gay members to remain celibate. The church still considers “homosexual relations” a serious transgression that can lead to disciplinary action, along with offenses like heterosexual sex outside marriage, child abuse, abortion and rape.

But the church has softened its tone toward gay members in the wake of protests criticizing its role in supporting California’s gay marriage ban. Church leaders here in Utah have held several meetings with gay rights advocates, and supported a 2009 anti-discrimination ordinance in Salt Lake City that protected people on the basis of sexual orientation.

Among the thousands of faces in the church’s “Meet Mormons” Web site — part of a national advertising campaign aimed at softening its image and showing its diversity — are a few gay members of the church. There’s Boyd from Alaska: “I am gay, Mormon and I believe in Christ!” There’s David (political junkie, huge reader, gay Mormon) and Rob (artist, dog lover, gay).

In 2010, openly gay students at the church-run Brigham Young University in Provo were allowed to set up a gay-straight alliance. In April, they produced a nine-minute YouTube video in which a dozen gay and lesbian Brigham Young students talk about grappling with the loneliness, fear and complications of being young and gay in a religion that prizes traditional families.

“What you are seeing is increased emphasis by church leaders on the need for our members to show sensitivity in this area so people don’t feel rejected, especially by their families,” Eric Hawkins, a spokesman for the Church of Jesus Christ of Latter-day Saints, said in an e-mail.

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But Mr. Hawkins said there had been “no shift or change in doctrine” on the church’s stance on gay relationships or the role of openly gay Mormons in their congregations. Sunday services are open to gay congregants, but members who want to hold leadership posts “must be living their lives consistent with the Church’s teachings,” Mr. Hawkins said.

It appears that many of the nation’s estimated six million Mormons agree with that position. In a Pew Research Center survey of Mormons conducted last fall, 25 percent said homosexuality should be accepted by society, while 65 percent said it should be discouraged. Fifty-eight percent of all Americans said that society should accept homosexuality, Pew reported in a separate survey.

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A few congregations do welcome gay members — an openly gay Mormon named Mitch Mayne even serves in a leadership position at his church in San Francisco — but advocates say that coming out still dislodges many gay Mormons from the church and their families. Reports of gay suicides, high rates of homelessness and drug abuse abound. In a 2011 survey of gay Mormons by researchers at Utah State University, most said their strongest feeling toward the church was sorrow.

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“There’s no place for gays and lesbians in the church right now,” said John Dehlin, a semiactive Mormon who has been critical of the church and helped organize the survey. “You have three options: celibacy for life, heterosexual marriage or excommunication.”

But that is beginning to change, said Joanna Brooks, a Mormon and professor at San Diego State University who blogs regularly about religion.

“There is a critical mass of people who want to stay identified with the faith and want it to be better,” Ms. Brooks said. “It’s a significant shift.”

Erika Munson, a mother of five from Sandy, Utah, near the doorstep of the Wasatch Mountains, never planned to become an activist. She felt sympathetic to the gay community, but had no gay family members and always separated her life as a Mormon from her views on gay rights. But she said she was “left shaking” by the church’s advocacy in California’s gay marriage fight, and saddened by years of watching gay teenagers vanish from the church after coming out.

So a few weeks ago, she set up group called Mormons Building Bridges to march in Salt Lake City’s June gay pride parade, and began sending invitations to friends from the church, telling them to wear “church attire” and comfortable shoes. She expected a few dozen people. Then 300 showed up.

Although some who marched that day said they had come to believe in gay marriage, the group was careful not to take a position on the issue, worried about alienating church members who supported greater acceptance of gays and lesbians but stopped well short of gay marriage.

“What our group is working for is to make a space for gay people in the church,” Mrs. Munson said. “There’s so much progress that needs to be made just at that level — to have them feel welcome and feel safe.”

In the living room of her expansive home in Salt Lake City, Ms. Stewart, whose husband runs an investment firm, described the delicate balance in situating her beliefs about gay rights and gay marriage with the church’s outlook. Even as she spoke about the need for a new direction, she was careful not to criticize the church leaders who decide those views.

“You live your life with faith,” she said. “Things are not O.K. right now, but it’s not the end. I value the organization of the church. I value the culture of the church. With faith, I hope things will change.”