A group of Mormon men sat around a coffee table at a house in Mesa, Ariz., on one recent September evening, debating a scenario that would have felt implausible just a decade ago: Could thousands of Mormon voters, disillusioned and disgusted by former President Donald J. Trump, help deliver a key battleground state to Democrats in November?

It’s already happened once. President Biden won 18 percent of Arizona’s Mormon voters in 2020, according to exit polls, a small but significant defection from a reliably Republican voting bloc that helped Mr. Biden flip the state blue by just 10,457 votes. Seeking their support for the third time, Mr. Trump appears to be dividing the state’s Mormons more than ever, according to interviews with a more than a dozen Mormon voters and state political analysts — which could give Vice President Kamala Harris an edge.

“People in my moderate circle of friends are watching and saying, ‘I can no longer do this,’” said Mike Badgett, one of the men in Mesa who was speculating about a greater shift toward Democrats. “I think the wheels are coming off of this agreement.”

Mr. Badgett was referring to the uneasy alliance between Mr. Trump and deeply religious voters. For years, many members of the Church of Jesus Christ of Latter-day Saints supported Mr. Trump, often reluctantly. They were turned off by his vulgarity, his disdain for women and his attacks on immigrants, anathema to the church’s pro-immigrant, pro-refugee message.

But they had been Republicans for generations, driven by a shared belief in traditional family values and Christian conservatism, and they were encouraged by his pledge to appoint conservative Supreme Court justices who they hoped would overturn Roe v. Wade and end the constitutional right to abortion.

It was one segment of a tacit understanding between Christian voters and Mr. Trump: They would ignore his character defects, and he would advance their policy priorities.