This is exactly what a guy on my floor at Georgetown did in 1979 - he was sick of the idea of a “Black Student Alliance,” and decided to create a “White Student Alliance.” Let’s just say that the administration took a rather dim view of that. They never did give him a straight answer as to why he couldn’t do it, or why he was wrong - they just said, “No” and threatened him with various non-specific punishments if he didn’t shut up.
He could have had a nice lawsuit on his hands. Probably just threatening to bring one would have made the administration cave, because even they would know it’s an open and shut case.