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“I think this is a big deal, and it’s an especially big deal because they’re both highly qualified, attractive, proven candidates with fundraising ability,” Mr. Monson said. “What you see around here is a lot of excitement among students in particular. And they’re already at work with both campaigns.”

That the LDS church has delivered two well-regarded candidates may say more about the candidates themselves than the church’s image within the political and social mainstream, he said.

“It’s not so much that the church is more or less accepted, it’s that you have two well-qualified candidates who happen to be LDS,” Mr. Monson said.

The church reissued a statement on political neutrality in response to the candidacies, saying that the church’s “mission is to preach the gospel of Jesus Christ, not to elect politicians.” At the same time, it issued a new statement June 16 noting that its full-time leaders “should not personally participate in political campaigns.”

The church showed its media savvy by refusing to be baited into criticizing “The Book of Mormon,” whose relentlessly obscene book both satirizes and sympathizes with its leading Mormon characters. While the show has plenty to offend the average Mormon, a church statement said only that the real book “will change people’s lives forever by bringing them closer to Christ.”

The church then launched a publicity campaign in Times Square showing posters of people of all ages and ethnicities announcing, “I’m a Mormon.”

Ordinary LDS members also appear to take the show and its hit status in stride.

Blogger Emily L., posting on the website, acknowledged she felt “uncomfortable” in two of the show’s dozen or more scenes, but added, “I saw it — and I lived to tell about it.”

“All in all, it’s vulgar, but fairly harmless towards the Church directly,” she wrote. “It has about as much impact as an episode of ‘South Park’” — the animated show that first made the authors of “The Book of Mormon” famous.

The church “is taking advantage of this to make people think better of them,” Mrs. Shipps said. “They are not dumb about things like this.”

One not-so-great Mormon moment came after the passage of California’s Proposition 8 in November 2008. Gay-rights advocates blamed the measure’s success largely on the involvement of Mormons, who contributed heavily to and campaigned for the measure banning same-sex marriage.

Mormons were targeted for protests outside temples and took a beating in the press. At the same time, their stance in favor of traditional marriage had the effect of improving their reputation with evangelicals.

What’s beyond argument is that Mormons showed themselves to be forces on the national scene. Whether they can string such moments into real cultural and political momentum remains to be seen.

“This does suggest that [Mormonism] has arrived as a mainstream topic. But you never know. These things ebb and flow,” Mr. Monson said. “It will be interesting to see what’s happening in 10 years, when there’s no presidential race or show on Broadway.”