Correct me if I am wrong, but I don’t think it is possible for a public university to be conservative.
I went to a large public university in Florida over 30 years ago. I think I got an excellent education and graduated with no debt. I was the sponsor of a company funded Engineering Research Project at my university and was at the final results presentation for all funded programs at the end of the university year two years ago. At a luncheon one of the students at the next table started spouting off about liberal trash. A professor at the table shut him down and criticized him about how ignorant he was. I still have some faith in the education in the hard sciences even at public universities as long as the student has good conservative grounding at home.
It is probably not possible for a public university to be conservative. It is possible for individual departments within a public university to be conservative. I suspect
that most business schools and engineering schools have a good number of conservative faculty, especially if they have had industrial experience before joining the faculty.