The Church of Jesus Christ of Latter-day Saints is about to find out.
For the last few months, a relatively small group of vocal, activist feminists (hereafter just ‘feminists’) have petitioned church leaders to allow women to pray in General Conference. Many members of the church were not aware that this was going on, and would be surprised that women had not prayed in conference before. Women pray in other meetings of the church, and have spoken in conference quite frequently.
Church leaders did what the feminists requested, and at the conclusion of the opening session of General Conference, a woman said a prayer for the first time. There was no special announcement for this, and for many members this was about as close to a non-event as it gets. I do think this was a big deal, but perhaps not for the reasons you might expect. I think this is a big deal because the church has now fed the feminists. Now what?
I do not expect for a moment that this act will permanently satisfy these feminists. Not by a long shot. I doubt that many of them will be satisfied until there is a female prophet. And now that the feminists have been fed, the protests will be louder, and more public. The pressure will only build. The most likely next step for the feminists is to seek ordination to the priesthood, which is an organized effort already underway.
That step would be so large, that it is difficult to imagine it being successfully taken. The Mormon Church is not the only church that does not ordain women, and many of the same biblical scriptures that the Catholics use to explain this, would be used by Mormons as well. Additionally, The Church of Jesus Christ of Latter-day Saints has D&C 107 which is hard to ignore. To me it would take a significant amount of feminist eisegesis to avoid the clear intention of a male priesthood in this canonized revelation. We also have this quote from the most recent prophet on the matter.
An emboldened group of feminists, and a church that is committed to a male only priesthood could make for an interesting few years.