Let me preface by saying I disagree with everything you say, but I still think you have the right to say it.

Universities are meant to be institutions of learning. Learning isn’t always comfortable. Some long held truths turn out to be wrong at some point. What we all think is true or right right now could completely reverse in a decade. Letting people speak especially when it’s against your morals is important for learning and understanding. Even if it’s bizarre and incoherent, if somebody believes it, we should try to understand why so that we can better educate those who were persuaded.

As an example of the rapid change in public thought and what’s acceptable, almost nobody publicly supported gay marriage a little over a decade ago. Saying you did would result in mockery, people questioning your sexual identity, people bringing up the religious history of America, etc. Now publicly opposing it is career suicide.

> Numerous private universities (Christian schools in particular) enforce strict student code of conduct rules that severely limit the student body's freedom of expression as to way to enforce religious or secular compliance. And it doesn't hurt their reputation but instead is an integral component of the school's identity.

Perhaps you're coming from a different cultural context than, but in my circles such universities absolutely are mocked and looked down upon. Some people don't even consider applicants from BYU, and other heavily religious universities because they don't want to reward such institutions.

> I know it's an unpopular opinion, but I'd argue that colleges and universities should have the right to police speech and expression: they should just be upfront about it. "Our house: our rules" as they say.

For public universities, the First Amendment legally obligates them otherwise. For private universities they already have the right to police speech and expression. It is, as you say, their house and their rules. They don't police (or rather they are very liberal in their policing) because freedom of speech and expression are central to an effective academy. Once universities start policing heavy-handedly, or on ideological grounds people start to doubt whether the ideas voiced are genuine or whether people are censoring themselves out of fear of retaliation from the institution. This cloud of doubt hangs overall the research published by that university, and the reputation of that university suffers considerably.