Here's my point:
- ICU's LGBTQ stance against BYU is in the "you'll have to deal with the consequences".
- NCAA transgender championship venues leaving NC is in the "consequences" category, but is also a little bit beyond that because it is in response to the new federal government nondiscrimination policy for public domain that can conflict with what some perceive as 1st Am.

Which brings us to the bakery example and how the B12 is (or can likely soon be) 'government' as much as the NCAA or a bakery.
- The bakery has proven that if the government deems an institution public domain and qualifies for nondiscrimination, then it trumps what some institutions would claim is right to act by conscience under 1st Am.
- If a bakery can be determined to be public domain, then certainly the NCAA and it's conferences can too, and member institutions will need to follow government policy.
- Under this scenario, the NCAA and B12 become 'government' in the sense that they are bound by government antidiscrimination policies (hence my earlier comment about B12 being 'government' as much as the NCAA or a bakery).
- BYU can remain an institution but not operate as it does currently in NCAA or B12 and is left to deal with that as a consequence.
- So you are correct that it is not a violation of 1st Am. rights of the institution to exclude BYU. BYU would have to deal with consequences of being self-selected out of the NCAA/B12. Some would then argue (like the bakery) that this is tantamount to government-based 'persecution' based on religion that violates the 1st Am. But the bakery lost. It can't operate as it was under the law because it is public domain. Churches are allowed to continue because they are not considered the same public domain. A private university sponsored by a church is somewhere between the bakery and a church.