SALT LAKE CITY — The Mormon church announced a campaign Tuesday for new laws that protect gay, lesbian, bisexual and transgender people from discrimination while somehow also protecting people who assert their religious beliefs.

“We must find ways to show respect for others whose beliefs, values and behaviors differ from ours while never being forced to deny or abandon our own beliefs, values and behaviors in the process,” a church elder, Jeffrey R. Holland, said.

Mormon leaders did not explain just how it would draw lines between gay rights and religious freedoms, and it’s unclear how much common ground the church will gain with this campaign. The church insists it is making no changes in doctrine, and still believes that sex is against the law of God unless it’s within a marriage between a man and a woman.

But the new approach could profoundly change political calculations in the Mormon strongholds of Utah, Idaho, Nevada and Arizona, where the church and its members play a large civic role.

In Utah, where most state lawmakers are Mormon, the announcement was cheered after years of failed efforts to pass anti-discrimination measures.

“What the LDS church did today was historic,” said Democratic state Sen. Jim Dabakis, who was raised Mormon and is openly gay. “This was a bold, strong, principled statement … today we are seeing the fruits of civility and respect.”

The gay-rights group Equality Utah also applauded, saying LGBT rights can co-exist with freedoms of religious people.

But national advocates on both sides were dismissive.

The Rev. Russell Moore of the Southern Baptist Convention called the Mormon leaders “well-intentioned, but naive” about animosity toward religious exemptions. And Sarah Warbelow, legal director for the Human Rights Campaign, called it “deeply flawed.”

The campaign is the latest example of a shift in tone on gay rights by The Church of Jesus Christ of Latter-day Saints, which counts 15 million members worldwide. They are preaching compassion and acceptance of gays and lesbians now that gay marriage is legal in Washington D.C. and 36 states including Utah.

“Accommodating the rights of all people – including their religious rights – requires wisdom and judgment, compassion and fairness,” said Holland.

Mormon leaders still want to hire and fire workers based on their religious beliefs as well as behavior standards known as honor codes,. The church also wants legal protections for religious objectors who work in government and health care, such as a doctor who refuses to perform an abortion, or provide artificial insemination for a lesbian couple.