Ms. Farr, 21, is part of the biggest gender change in the Church of Jesus Christ of Latter-day Saints in memory. After the church lowered its age requirement for female missionaries in October 2012 to 19 from 21, so many women have signed up — 23,000, nearly triple from the total before the change — that many Utah colleges suffered sharp drops in enrollment, and the standard image of a Mormon missionary, a gangly young man in a dark suit, was suddenly out of date.
In the coming years, these women are expected to fundamentally alter this most American of churches, whose ruling patriarchs not long ago excommunicated feminist scholars and warned women not to hold jobs while raising children. Church leaders have been forced to reassess their views because Mormon women are increasingly supporting households, marrying later and less frequently, and having fewer children. And for the first time, waves of...