It's not ethical and logistical contortions. There are multiple possible reasons. First, it's possible your underlying assumption (that the Pac-12 didn't let BYU in because of BYU's religion) is false. I know it's considered a truism on this board, but it's possible that the research requirements are real, not just covering for religions discrimination. If that's true, then it requires absolutely no contortions to hire a member of the LDS faith.

Second, it's possible that if that underlying assumption is true, that it's only a problem for a handful of schools, and some schools aren't on that list. Those schools can hire members of the LDS faith with no contortions.

Third, even if both of the above are incorrect, it's possible that the objection the BYU on religious grounds is a concern with the institution of the church, and not a concern with individuals who are members of that religion. That the issues of gender dynamics, LGBT activism, the ethical concerns about religions being tax exempt, etc. are institutional, and not personal in nature, and that if so it takes no contortions to hire a member of the LDS faith.

Finally, even if all three of the points above are incorrect, it's possible for a school to decide that none of their concerns about an individual's faith have anything to do with being a football coach, so they don't worry about it.