I won't say anything more than this on this thread, if you want to respond, just copy and paste your response to the appeals thread.
But no, no they cannot kick people off of teams for reasons that would violate the Constitution.
You're right, they could lie and say they are kicking them off for another reason, but then you see you are making my point. They cannot kick someone off for whatever reason they want.
Tactically, if one of the accused is exonerated by the appeals process, it would be incredibly dumb for the school/team/department to kick the player off the team for a violation of team rules. You open yourself up to an incredible amount of liability if you fire someone/kick someone out of school/remove a scholarship for a reason that would violate the Constitution and you had the audacity to try to circumvent that core American principle.
It's almost like a whistleblower in a company, that company better not fire that person after they've come forward.