As Republicans across the country contend with the fallout from a newly released recording in which Donald J. Trump made vulgar and sexually degrading comments about women, perhaps nowhere was reaction more swift and decisive than in Utah, home to a sizable Mormon population already deeply unsettled by a sense of the candidate’s moral shortcomings.

Within hours of the video’s release on Friday, a number of top Republican officials in the state yanked their endorsements, including Gov. Gary Herbert, a Mormon, who declared Mr. Trump’s statements “beyond offensive and despicable.” Representative Jason Chaffetz, who is also Mormon, said that if he voted for Mr. Trump he would no longer be able to look his 15-year-old daughter in the eye.

On Saturday, the Deseret News, a media outlet owned by the Church of Jesus Christ of Latter Day Saints, broke with an 80-year tradition of refraining from presidential endorsements to publish an editorial calling on Mr. Trump to step aside.

“We prefer to stand for something rather than against someone,” Deseret’s editorial board wrote. “But this is one of those rare moments where it is necessary to take a clear stand against the hucksterism, misogyny, narcissism and latent despotism that infect the Trump campaign.”