witness of their most sacred spiritual feelings for 2 years to strangers, and then do it again throughout their lives once a month to their neighbors ... is a religion that shames men for emotion?
I think you're completely wrong here.
Look, men in GENERAL don't show much emotion. That's not an LDS thing. So first of all, throwing this on a church culture thing is, I think, weird.
Second, I don't think this is the problem BYU has in the NCAAs at all.