The legal situation is very different between a private university and a state university.
Private entities are protected by the First Amendment while state government entities are restricted by it (technically as incorporated by the Fourteenth).
Conflating the two situations just leads to confusion.
The legal situation for private non-profit universities (particularly those without religious affiliation) is quite a bit more complicated than anyone on this thread seems to realize, mostly for statutory reasons. Maybe with the exception of Hillsdale and a few others.
I have honestly no idea what SCOTUS would do with these cases absent an agency rule or legislation banning DEI statements, for example, and IMO anyone who claims otherwise is a clerk, a SCOTUS judge, married to a SCOTUS judge, or lying :)
I am fairly confident that state legislatures could ban DEI statements at public universities, but I am also fairly confident that this wouldn't actually change anything and that people who think otherwise haven't ever been a serious applicant for a faculty position.
Private entities are protected by the First Amendment while state government entities are restricted by it (technically as incorporated by the Fourteenth).
Conflating the two situations just leads to confusion.