They do embrace diversity of though and allow speech of those who happen to disagree with the majority. The problem is that colleges also encourage critical thinking and evaluation of the thoughts expressed. This is why colleges seem so liberal, not because of indoctrination, but because right wing thinking tends top wither and die in the face of critical evaluation.   

As far as "shutting down opposition" that is not the school, it is the students. In cases like Milo and Ann Coulter, students are well aware of the hateful and bigoted rhetoric spewed by both and decided that those speakers and ideas are not worthy of a platform. I don't agree with preventing the speeches but I understand why they did it. After all freedom of speech does not mean freedom from derision and scorn. No violation of the 1st occurred since it was not the government that silenced the speakers.