The university does not accept federal funds except on a quid pro quo basis, meaning they might accept a particular federal contract for specific results. No federal funds are accepted for general purposes. Many years ago the feds tried to argue the university was bound by all the usual federal regulations applying to federal funds if it had even one student attending who used Pell Grants or federally insured student loans. That battle was fought and won by the university but, as the battle was going on, the university seriously considered how it might help students in the event it had to prohibit those grants and loan guarantees. With Obama cutting banks out of the student loan process, I suspect the issue will rise again.
IIRC, the ACLU was involved and was trying to sue to have BYU do the whole co-ed dorm thing. BYU wouldn’t give an inch and the ACLU caved.