Assuming (a) no taxpayer money is involved and (b) they disclose that being woke is a condition of admission, they should be able to do anything they want. They can be the Hillsdale College of the left, as far as I would be concerned. BUT, big but, if they receive taxpayer money and if they claim to have academic freedom, they should be held accountable.
Which is why Hillsdale no longer received federal funds starting in 1984-85 school year and from Michigan in 2007-08.