and they also value academic freedom. I'm wondering if faculty in the P12 wouldn't just call their peers at UT and point out their problem with BYU.

I don't think the P12 is anti-BYU. They value academic freedom. People have pointed out how there are plenty of BYU grads at P12 schools. They don't want their conference associated with BYU because faculty at BYU don't have full academic freedom.

They may also dislike the honor code since it goes far beyond the normal academic honor codes that every school has. But the limits to academic freedom aren't as nicely spelled-out as the honor code is.