One thing that I don't think has really been internalized by enough folks is that /any/ direct citizen-police confrontation is dangerous, and in the US, due to gun and police issues, can be very dangerous or deadly. Calling in cops doesn't mean someone /will/ die. But it does mean someone /might/.
If you're president of a university and there's a protest you don't like, do you call the cops? Look. Put aside the first amendment stuff. That's great. It matters later. It's not the important thing in the instant: what matters is you're creating a situation that is actively dangerous for students
And for what? For a rule? Who gives a shit? Boo-fuckety-hoo. If the protest is peaceful--and to be clear, the conversation becomes less clear-cut very quickly if it is not--then why are you putting students at risk to punish their defiance? That's putting your feelings ahead of their safety
I wonder whether some of this is driven by a concern about future protests and viewpoint discrimination. If they allow these protestors to stay and then a bunch of Proud-Boys-aligned students set up next, I assume the school has to treat them to same way if their protest behavior is the same.
Protests that violated campus rules in a similar way? I think that's the key question. If you have rules but enforce them in a viewpoint discriminatory way, that's a 1A violation. (Though Columbia doesn't have to adhere to 1A, obviously.)
So maybe I just answered my own question! Columbia could simply decide to enforce the rules against a future Proud Boys protest but not against this one. A public university couldn't.
I also suspect they’re worried about several things at once:
-general safety (avoiding a mass shooting, assaults, etc)
-avoiding other bad conduct in the campsite
-defending against hostile environment discrimination claims