but playing at BYU has made an athlete's church membership much more well-known by the public at large and a larger talking point throughout their career, professional as well as collegiate.
The question of whether it would not be a factor at all is a false dichotomy. The comparison is the relative benefit or attention to the church and it's not close.
If you think additional attention to the church via athletics is an important benefit, then the OP is right.
If you don't, then it's just weird and people should play wherever they want.