Feel free to be a 1st amendment extremist if you'd like...
My position is actually not extreme at all. I'm not advocating for any change or extension of the already established rules. I'm saying that it's a bad idea for universities to violate those rules.
You're the 1st amendment extremist here. You're the one saying that the 1st amendment protects too much speech and needs to be curtailed.
You don't think public schools should be seen as government entities. That's a fine idea to have, but here's the deal: the rules say that they are. The rules say that students can wear black armbands to school in protest of the vietnam war, and they can call police "motherfuckers" on campus, and they can have and share any number of other controversial opinions. If they did these things at MCC, then the students could get expelled. But at K-State and Alabama and MHS and every other public school in the country, students have speech rights, and those speech rights include speech that you and i find reprehensible. Those are the rules.
Viewing the university punishing this girl the same as state sponsored censorship is amazingly nearsighted and narrow.
That's exactly what happened here though. The university didn't like what the girl said on her snapchat so they expelled her. Your position would also permit schools to expel students for attending a BLM march. Obviously you and I agree that attending a BLM march is "better" than dropping racist remarks on a snapchat, but 60 years ago, a significant portion of society would've come out the other way.
Allowing schools to pick and choose which viewpoints their students are allowed to have is dangerous. Saying "ok don't make controversial/disruptive racist remarks or you're expelled" opens the doors to public schools expelling students for any other disruptive viewpoints that may have actual worth (i.e. the Missouri protests). In my view, it's better to not discriminate based on viewpoint, and to have enough faith that "better" ideas will prevail over "worse" ones in the general discourse. This isn't a radical or extremist view - it's the backbone of what "free speech" means and why we have it.
It's honestly a little surprising to me that you're being so shortsighted here.