Because it’s a state school, the First Amendment protections are stinger than if it were a private one.
The National Fraternity did the right thing in shutting the chapter down. They also did the smart thing by beating the school to the punch in doing so.
That having been said, this would appear to be an explicit admission by the chapter and a number of its members that they engage in racial discrimination in choosing their membership. Which isn’t protected by the First Amendment. If I was part of the school administration THAT’S the angle I’d be pursuing.
Stronger, not stringer ...