To get the official Mormon response to the Broadway musical smash “The Book of Mormon,” you can check out the program for the Paramount Theatre’s Seattle run of the show, which opened Tuesday.

In Seattle and other cities the show is visiting, the Church of Jesus Christ of Latter-day Saints is taking out full-page ads in the theater program — not in protest against the musical comedy, but as a way of reaching the hundreds of thousands of patrons who’ve been flocking to see “The Book of Mormon” in venues across the U.S., including in Los Angeles, Chicago and Portland.

The church’s reaction may seem a bit incongruous, given that “The Book of Mormon” is a wholly irreverent, often-raunchy musical satire about a pair of squeaky-clean and clueless young Mormon missionaries sent off to spread their religion in AIDS-stricken, poverty-ridden Uganda.

Winner of nine 2011 Tony Awards, including one for best new Broadway musical, and a box-office phenomenon wherever it plays, the uproarious show is the brainchild of non-Mormons Trey Parker and Matt Stone (the creators of TV’s popular and often controversial animated sitcom “South Park”), and Broadway composer-lyricist Robert Lopez (“Avenue Q”).

The team’s take-no-prisoners brand of comedy skewers homophobia, racist attitudes and cultural myopia in the Mormon church, as well as many other touchy targets.

Yet the response of the Mormon religious establishment to the wildfire success of “The Book of Mormon” seems to be: If you can’t beat ‘em, welcome ‘em.

“We recognize that the musical is a satire and that it pokes good-natured fun at The Church of Jesus Christ of Latter-day Saints,” says Annette Bowen, co-director of Greater Puget Sound Public Affairs Council of the Church of Jesus Christ of Latter-day Saints.

“The Book of Mormon” has been lauded by critics and fans for its edgy humor and musical parodies, but also for its “sweetness” and affection toward the two main characters on a mission: the gung-ho, goody-goody Kevin, and Arnold, the graceless but lovable “Star Wars” geek.

Bowen agrees the show “isn’t an entirely accurate portrayal of our missionaries or the residents of Uganda as we understand it. Nevertheless, the production has been reported as being generally good-willed about Mormons, for which we are grateful. Plus, the play has prompted many questions and inquiries about our church and beliefs. We’re always happy to answer questions.”

“The Book of Mormon” has, indeed, created a new opportunity for the LDS church to publicly reframe an indigenous, messianic American religion founded in the 19th century by Joseph Smith.

Mormons now constitute one of the fastest-growing religious groups in the U.S., with more than 6 million people in the fold — the vast majority of them living outside Salt Lake City, Utah. (About 270,000 live in Washington, according to the church.) Yet to much of the public, LDS history and beliefs, rites and rituals are still a source of mystery, curiosity, even suspicion.

Thanks to a higher Mormon profile in political and cultural arenas, and a publicity campaign by the church to “normalize” its image, America is experiencing what some LDS arbiters call a “Mormon moment.”

The sophisticated national “I’m a Mormon” ad campaign by the LDS church, aimed at demystifying the church and encouraging people to learn more about it, also sparked new awareness of the religion.

But representations of Mormons in mainstream popular culture are salient factors, too — even when those representations are as outrageously spoofy as in “Book of Mormon.”

“I do think the fact that you can make fun of Mormons now, and some Mormons are able to laugh at that, is evidence of a growing maturity and assimilation into American culture,” Hagland says.

Even before “Book of Mormon” was busting box-office records on Broadway (where it has grossed $136 million in less than two years), and selling out in other cities (including Seattle, where only a smattering of tickets are still available through day-of-show lotteries), a couple of other vivid fictional works thrust Mormons into the spotlight.

The 1993 Pulitzer Prize-winning play “Angels in America,” a complex, lauded work by Tony Kushner, and the HBO miniseries based on it, delved into aspects of Mormon theology and history unknown to most Americans, and portrayed the church’s longtime intolerance of homosexuals in its ranks.

One of its three LDS characters was a conservative, married lawyer whose Mormon beliefs clashed with his closeted homosexuality. Some church members objected to Kushner’s profile of the religion, and were offended by a scene where the special undergarments that devout adult Mormon men often wear, which is considered a private, sacred practice, were shown.

Drawing more attention for its depiction of Mormons was the HBO television series “Big Love,” which ran for five seasons, starting in 2006.

It focused primarily on two fictional (and illegal) polygamous Utah clans. One was an extended suburban family led by a successful businessman seeking to establish modern polygamy within mainstream Mormon society; the other, a backward rural “compound” led by an abusive patriarch.

The LDS church issued a harsh critique of “Big Love,” objecting to its “unhealthy preoccupation with sex, coarse humor and foul language,” and its depiction of secretive Mormon ritual in an episode. Others slammed the series for creating false stereotypes that don’t mesh with the modern-day Mormon majority.

“For most mainstream Mormons, ‘Big Love’ would seem almost as alien as it does to everyone else,” said Hagland. “It’s been more than a century since the Salt Lake City-headquartered church sanctioned polygamous marriage, and those characters seem like very distant cousins.”

By comparison, “The Book of Mormon” has been greeted warmly - and, perhaps, with relief. That’s despite objections to the profane dialogue and deliberately tasteless buffoonery that have kept many church members from seeing it.

Says Hagland: The show “is about nearly every Mormon’s brother, son, nephew, best friend who went on a mission. It hits close to home. And it explores, or at least mocks, foundational Mormon stories and doctrines that can’t be dismissed as mere cultural oddities.”

Despite a title that refers to a sacred LDS text, there isn’t much actual Mormon theology in the musical. The exception is the song “I Believe,” in which Kevin affirms his fidelity to some “quirky” beliefs associated with Mormons - such as “ancient Jews built boats and sailed to America” and that “the Garden of Eden is in Jackson County, Missouri.”

Hagland laughs off the song as “good caricature,” but applauds “Parker and Stone for really nailing the Mormon sweetness, niceness, and sense of do-gooderness. That’s real. And part of why the church has responded well to the show, at least officially, is because that affection comes through.”