In which state do young couples get married, stay married and have many more children than any other? That’s right. It’s Utah, headquarters of the Church of Jesus Christ of Latter-day Saints, a religion that puts a heavy emphasis on home and hearth and on traditional families that endure forever. According to church authorities, men’s and women’s spheres are separate, as decreed by God.

“By divine design, fathers are to preside over their families in love and righteousness and are responsible to provide the necessities of life and protection for their families. Mothers are primarily responsible for the nurture of their children,” according to the 1995 LDS document, “The Family: A Proclamation to the World.”

And — trick question — which state has one of the highest rates of women with young and school-age children employed outside the home? Stumped? It’s Utah. Mormons need to pay the bills like everyone else, and in this economy, pragmatism — another Mormon virtue — trumps whatever idealized vision of family life the LDS leaders might hold.

As Mitt Romney, who among other things is a Mormon traditionalist, continues to struggle to find his footing among female voters, his church is undergoing a dramatic social upheaval led from the grass roots by its women. In this “Mormon moment,” the popular images of the LDS Church — epitomized by the Romney clan and satirized in the play “The Book of Mormon” — are of scrubbed and square golly-gee Ozzie-and-Harriet types. But in real life, a new generation of LDS mothers and wives is visibly struggling with the conflicting messages they’re sent by their church and society, actively trying to figure out how to stay faithful while putting food on the table — and sometimes, even, finding professional fulfillment outside the domestic sphere.

“If you compare the church now to 30 years ago, there’s much more acceptance for women to have a career and to have children, too, but there’s tension and a mixed message. Women feel it, and it creates a lot of guilt,” says Margaret Toscano, a professor at the University of Utah who was excommunicated from the LDS Church in 2000 for her feminist scholarship.

The revolutionaries have many faces. Joanna Brooks, author of the memoir “The Book of Mormon Girl,” is the most prominent of this new group — she travels the lecture circuit, has appeared on Jon Stewart’s show and opposes her church authorities most visibly in her support for same-sex marriage — but she is not alone. Groups of Mormon women (and men) are, like their Catholic sisters, organizing to lead a charge for women’s ordination (although within the church they are seen as radicals). Last month, a panel of Catholic and Mormon feminist scholars met at Claremont Graduate University in California to discuss the subject.

Far more moderate is the Web site Feminist Mormon Housewives, where faithful Mormon women push back against their church’s sexual and lifestyle strictures, including its prohibition against masturbation. They confess to their belief in abortion rights, argue for better female representation in the church’s missionary program (foreign missions have traditionally been a rite of passage reserved for men) and wonder aloud how Republican social policies will help them, as one stay-at-home-mother-blogger put it, “should my husband get hit by a bus on the way home from work today, or leave me for a younger, prettier woman, or go insane and try to kill me, or crush his leg and lose his job and need me to take care of him 24-7.” (“Preach it, sistah!” responded one commenter.)

Last year, on a Web site called Mormon Perspectives, Lisa Tecklenburg, a 31-year-old, unmarried Mormon with an MBA who works as a brand manager at Procter & Gamble, argued that “The Family,” cited above, “does not necessarily mean that women have to stay home. In fact, the world is quickly adapting to enable more women (and men) the ability to enjoy working and being able to spend desired time with their children.” And though the church has historically disapproved of women’s ascent in the corporate world, those days are over. In the future, Tecklenburg wrote, “the business world will see more and more Mormon women rise in the ranks along with women of other faiths.”

In an interview, Tecklenburg added that Mormon women are not unlike other women: “We feel the desire and the drive to do all these things, and we feel we can do them,” she told me.

In an effort to get ahead of all this dissent, LDS church HQ is now running on its home page a two-minute ad called “Daughters of God,” which shows Mormon women in their traditional roles, yes, snuggling children and doing volunteer work, but also biking, running, performing surgery, standing at a lectern before thousands, wearing a cap and gown, and working in an office cubicle. “I have unlimited ability,” the ad says. “I am un-stoppable . . . I am a leader . . . I am a Mormon woman.”

Perhaps Romney’s disconnect from female voters, then, is rooted in a vision of gender roles he has been taught since childhood. If that is the case, he might look back to his church for a course correction — for there, even within the confines of a strict patriarchal hierarchy, faithful Mormon women are asking all the right questions about how to live.

Follow Lisa Miller on Twitter: @lisaxmiller