I don’t think BYU will ever be able to join the P12 for the reason provided but I do not believe that religion alone will keep BYU from a B12 or SEC invite (not that they’d actually get one). I just think the ultra progressive attitude in the West is different from the more open and relaxed attitude in the South.
I do believe religion has played a part in keeping BYU out of the B12 but it hasn’t necessarily been a non-qualifier.