Institutions with distinct missions from BYU. I can see why cal and Stanford (and the other liberally minded research schools) would foresee nothing but headaches from BYU. There are a dozen reasons why BYU would clash with those schools in everything from corporate governance to scheduling to academic compatibility.
On the other hand, BYU is quite similar to existing big 12 teams. The big 12 just didn’t want mormons in their conference.