No, they should not.
Trying to have it both ways is killing everything. Pick one and only one.
If someone says universities indoctrinate then they simply have no business attending one. If they attend one, then they get what they deserve, good and hard. After all they did pay for it.
Alito attended Princeton and Yale.
Clarence Thomas also went to Yale Law School.
Liberal? Yes. But for now, it’s the game we have to play.
As I indicated above, I would be OK with cancelling the Truman Scholarship, or at least withholding the Federal portion of it which is likely nearly all of it.