Public universities generally can't punish students based on what the students say. That's true even if the student's speech is deeply offensive to many. Public universities are branches of the government and thus bound by the First Amendment. The Supreme Court has repeatedly held that public universities can only restrict speech based in its content in a handful of narrow, traditionally recognized exceptions.
Classic examples of such unprotected speech are true threats of illegal conduct, intentional incitement to imminent and likely lawless action, and face-to-face targeted personal insults that are likely to start a fight. There is no exception for supposed hate speech or even for advocacy of genocide. Students are free to call for the destruction of Israel or for an even more forceful response by Israel and Gaza.
If Iran detonates a nuclear bomb in Israel, students would be free to call for Israel to do the same to Iran, even if that means killing a vast number of Iranians. Likewise, in a future China Taiwan conflict or some other foreign war. War and the mass killing it brings are regrettable facts of international affairs, and all Americans, students or not, have the equal right to defend and criticize acts of war.
Private universities aren't bound by the First Amendment as such because the First Amendment only applies to government actors. But many private universities have voluntarily adopted policies committing themselves to follow First Amendment principles. The private Yale University might not want to be seen as providing less protection than the public university of Connecticut.
Indeed, California even has a state statute extending First Amendment protections to private university students. So in practice, most private universities respect student free speech rights in much the same way as public institutions. The temptation to censor speech we hate is strong and understandable, but it's also dangerous. If we support censoring speech that offends us, eventually the views we support will be censored too.
The best way of dealing with evil ideas is to argue against them, not to suppress them. Such counter speech isn't a perfect solution, but it's better than the alternatives. To be sure, many universities have given in to the temptation to restrict speech in recent years. Suppressing speech that some claim was racist or anti-gay or anti-trans or what have you and part of human nature is what I call censorship envy.
Once speech that offends one group is blocked, other groups will seek similar restrictions on speech that offends them. After all, who wants to be the chump who goes along with free speech principles when others are getting away with suppressing speech that they dislike? The solution to this sort of inconsistency, though, is to return to equal freedom of speech, not to level down towards equal suppression.
But even public universities can impose content neutral restrictions on the time, place, and manner of speech. They can, for instance, ban demonstrations that are unduly loud or that block entrances to buildings. They can ban destroying campus property, physically assaulting invited speakers or fellow students or occupying offices. Likewise, universities can forbid students from camping out in public spaces.
Public spaces are supposed to be open to all students, not to some small group that chooses to take them over for its own purposes. But all such rules must be evenly applied based on what is being done, not what is being said. The same rules should apply whether it's a conservative group, a liberal group, or anyone else.
Indeed, if a public university applies such rules in a content-based way, that itself would violate the First Amendment. Any restrictions that we support will soon be used by officials with whom we sharply disagree. Content neutral restrictions that apply equally to everyone may make sense, whoever is applying, but the power to suppress student speech based on its message is a dangerous power, one we shouldn't give to university officials any more than to other officials.