Over the past five years, the Church of Jesus Christ of Latter-day Saints has worked feverishly to burnish its reputation. Stung by the backlash to its support for California's Proposition 8 banning same-sex marriage, the church has modulated its rhetoric about sexual orientation. In reaction to calls for greater equality for women within the church, Mormon hierarchs have invited female leaders to sit amid their male counterparts and deliver public prayers at general conferences.

Nevertheless, last week two members of the...