I've recently heard some people (serious people, though not First Amendment experts) argue that private universities have a duty to suppress certain kinds of anti-Semitic speech—or perhaps, more broadly, anti-Israel speech—when it creates a "hostile educational environment" based on national origin. Title VI of the Civil Rights Act of 1964 bans race and national origin discrimination in federally funded programs, and courts have read that as requiring such programs (including at universities) to prevent such hostile environments. And, this particular argument goes, applying this legal requirement to anti-Semitic/anti-Israel speech doesn't violate the First Amendment because the First Amendment doesn't apply to private universities.
This argument, I think, is wrong, because it misunderstands the nature of the "state action" doctrine. It is true that the First Amendment generally doesn't protect speakers against private action (by private universities, private employers, private social media platforms, and so on). But it does protect speakers against government action, and the threat of civil liability (or withdrawal of federal funds) under Title VI is government action. And this protection extends even when the speakers are on private property.
Consider a few familiar examples. Does the First Amendment protect speech in ads in the New York Times? Well, it doesn't protect such speech from the Times' editorial decisions; you and I have no First Amendment right to force the Times to carry our speech. But when the government imposes civil liability on such speech, that civil liability may violate the First Amendment, because it's the government that's imposing it. Those are, of course, the facts of New York Times Co. v. Sullivan (1964); note that the defendants there weren't just the newspaper but also the individuals responsible for the advertisement.
