No one has a right to form a student group, and a school could legally forbid them. But once a school allows some students to organize along certain lines (in this case racial lines) disallowing other students from doing the same is an affront to the rights of those students. For instance under the equal protection clause it is impermissible to say “for Whites the rule is A but for Blacks the rule is B.”
It may be hypocritical, but not disparaging of their rights, which aren’t at issue. Either students have a right to form officially recognized groups of their choosing or they don’t, and they don’t. They don’t suddenly have a right because you think the school’s student group policies are inconsistent, inappropriate, or irrational.
What’s at issue is the justice or rightness of the policy. Though rights are part of justice and, obviously, rightness, they aren’t the whole of it. We carry ourselves away with rights talk, when often all we really mean to do is talk about morals, ethics, justice, etc. As you figure it either groups can be formed on the basis of race or not, and any forebearance of certain racial groupings is unjust. Okay, and I agree, and certain that argument has compelling logic. But of course you must be aware of the prevailing view of “diversity,” whereby nonwhites segregating themselves are good and whites bunching together is always bad. However wrong is this view, whatever bad results we’ve seen in the past, it comports with most people’s, and certainly academia’s, sense of justice.
So we re left with competing views of the good. If it’s a private school you may refuse it tout tuition and persuade others to do so. If it’s a public school you may appeal to higher justice, namely antidiscrimination law. Good luck, given judges’ sense of justice. All I’m saying is rights don’t enter into it.