Which makes one wonder what Romney himself would think of the show. In public, he's been good-humored. In private, would he fume?
Or would he realize that The Book of Mormon, blasphemy and all, is precisely the kind of public-relations tool that Mormon candidates could use?
Mormonism looms over Romney's presidential prospects today, just as in 2008, except now there are two major Mormon candidates. For Romney and Jon Huntsman, the path to the presidency is: Appease evangelical Christians to win the nomination, then assuage social liberals in the general election. (In a recent Gallup poll, notes Southern Methodist University's Matthew Wilson, more Democrats than Republicans said they would never vote for a Mormon.)
So far, Romney and Huntsman have taken very different approaches. In his speech on faith in 2008, Romney defended his devoutness and argued that Mormons are not different from other Christians. Huntsman has played down his Mormonism, saying several faiths play roles in his life.
The nation's fourth-largest religion has been prominent of late. The church played a major role in supporting California's gay-marriage ban. It has been having a pop culture moment.
And when it comes to depictions of Mormon life, The Book of Mormon is, in some ways, the most accurate. HBO's Big Love and TLC's Sister Wives focus on polygamy, which the church has disavowed for a century. In The Book of Mormon, the subject doesn't come up. Robert Lopez, who cowrote the show, told me that it once had a single polygamy joke. It didn't get a laugh, so it was cut.
Yes, the show pokes fun at Mormon customs, such as the church's ban on coffee and tea. (In a raucous dream sequence set in hell, Hitler and Jeffrey Dahmer dance with a pair of giant coffee cups.) It paints young Mormons as repressed in a tap-dancing number called "Turn It Off."
But it also paints young Mormons as wholesome, optimistic, well-meaning, and all-American. It focuses on the Mormon mission, a rite of passage that's a character-building credential in itself, says Nathan Oman, a law professor at the College of William and Mary who spent his own mission in South Korea.
The mission, Oman said, teaches responsibility, service, humility, and an expansive view of the world. The Book of Mormon even makes a case for proselytizing - if the alternative is, say, a culture that allows female circumcision.
Ultimately, the show takes a sunny view of the Mormon faith, and faith in general. Its main point is that religion can be a powerful positive force if no one takes the backstory too literally. And that Mormonism is really no stranger than any other faith - which is in keeping, in a way, with what Romney argued in 2008.
Lopez said he trusted Mormons would take the show well. Evangelicals launch cultural wars; Mormons let things pass. "Part of the reason we like them so much," he said, "is that they take the same view that we do, which is that the First Amendment takes care of all of this stuff."
Indeed, the church's statement on the show was benign and slyly evangelical: "The production may attempt to entertain audiences for an evening, but the Book of Mormon as a volume of scripture will change people's lives forever."
And whatever he thinks, Romney has, wisely, stuck to that message. "You know your faith has finally made it big time when people are poking fun at you on Broadway," he told NBC. The best way to prove that you're like everybody else is to show that you can take a joke.
Joanna Weiss writes for the Boston Globe.