You're right, but the university is not allowed to censor student speech based on content. The "actions" that the administration claims the university should have taken would have violated the constitution.

Furthermore, the redresses the administration has proposed in similar cases (like the university reporting students who protest to federal authorities) suggest this is more about federal power / censorship than furthering universal free speech.

> the university is not allowed to censor student speech based on content

Hold on, didn't tenured professors get fired literally based on content of their speech a few years back under the other administration? I am confused

And this does not have to be about censoring speech. There are rules of a place. As I said, you start obstructing a lecture, you get thrown out in a good university

I don't think this is quite correct, at least for private universities. They absolutely have the right to disallow protests on their property. The first amendment protects you from the government -- the government cannot force the university to take these action, but the university could totally do it on their own. It's a little bit murkier with state universities, because you could argue they are a part of the government.