Any of those would understandably be pretty abhorrent in an institutional environment that places a high value on scientific knowledge and critical thinking.
If what you’re referring to is the finding that “Students across political perspectives engage in classroom self-censorship”, I don’t think that’s anything new either. Students are almost always wary of expressing controversial views in a classroom setting, and even those who feel confident that their views are considered the normal majority position in that environment have some fears about rocking the boat.
It’s quite true that liberalism of some form is considered “the normal majority position” in higher education to a much greater extent than it is in the society at large. But that was true forty years ago too. MAGA’s not popular on campuses now; the “Moral Majority” wasn’t popular on campuses back then.
That, perhaps, may explain some evolution in the nature of conservative parents’ fears, if the change that you ask about in your OP is really a thing (not being a conservative parent myself, or knowing any conservative parents very well, I don’t have my finger on that particular pulse).
In my young day, the mindset of conservatism was heavily enmeshed with what we still occasionally called “squareness”. Conservatives self-identified as supporting “family values”, religious traditionalism, quasi-authoritarian patriotism, conventional careers, etc. What conservative parents feared (at least, according to the comparatively few people with conservative family backgrounds I knew in college) was that their kids would be lured away by the appeal of the “lifestyle” of “hedonistic”, sex-having, substance-consuming, art-class-taking, swear-word-using, hair-growing liberals.
Then came Rambo, and the rise of the “antisocial conservative” hero figure in general. The conservative self-image shifted (not entirely, but substantially) toward the “badass lone wolf” model, the beleaguered and disillusioned (but extremely cool, unlike his “square” predecessor) anti-hero type, who has to fight to survive in a hostile environment. (Mad Max is another avatar of this transition.)
So we segue from Moral Majority to militias and then MAGA. A significant chunk of conservatism is radicalized and aggressive, perceiving itself now as the “outsider” rather than the dominant “establishment” (despite the fact that people who identify as conservative, especially conservative white men, still have hugely disproportionate power in our society). Moreover, many self-identified conservatives nowadays are having, or at least think themselves entitled to have, all the sex and drugs and swearing and hedonism that they want, so the seductive-sinfulness aspect of the so-called “liberal lifestyle” is not really an issue for most of them.
So maybe that’s the zeitgeist that some conservative parents are experiencing? They perceive their kids as heading off into the “liberal environment” of college, not like a Mormon missionary crossing paths with a Mardi Gras parade and about to get his personal purity seriously tested, but like Jack Reacher or somebody walking into a den of villains who are out to get him.
Just a speculation.
Say that to many pro-gun-rights conservatives, and you’ll get complaints that you’re “vilifying” and “silencing” them and making them “self-censor” with your “disparagement”. Reacher needs his guns, you see: the world is a dangerous place, especially for freedom-loving non-conforming badasses like him.