I don't necessarily agree with tossing such resumes in the garbage, but it is evidence that universities that enforce religious dogma on their students do suffer a hit to their reputation because of that.

> how do you explain the strong performance (and reputation) of private institutions vs. "state schools"?

Not every private school is Stanford, MIT, etc. Plenty of private schools are shitty for-profit enterprises (especially online universities) that essentially scam customers out of their money. Purely on the basis of return on investment many studies also conclude that public university is better than private universities.

Also most reputable private university do respect freedom of speech and expression to a similar degree as public universities. If you factor in the reactions of students, perhaps even better. When Berkeley hosted Milo Y students rioted, smashed up cars, etc. When Stanford hosted Dinesh D'Souza it was very tame with protesters being non-disruptive. Public universities aren't immune from going off the deep end regardless of constitutional protection: https://www.youtube.com/watch?v=2cMYfxOFBBM

Again, the private schools with good reputations do behave almost as if the First Amendment applied to them. The ones that don't generally aren't reputable. So your question is based on false premise.

Education is not some kind of of enterprise free from regulations. The consequences of bad education is similar to bad health care. As I see it, let schools worry about education, political system deal with politics, legal system deal with enforcing the law, health system deal with health issues, and religious communities deal with religion. Trying to mix them together will only cause intolerance and tensions in society.