Public colleges and universities are bound by the First Amendment. Their private counterparts are not (though a state might choose to apply the requirements of the First Amendment to them, as California has largely done). But if private universities choose to follow the First Amendment, they will make life a lot easier, and also a lot better, for faculty, administrators, and students alike.
One reason is that First Amendment principles make most cases easy.
The First Amendment does not protect plagiarism, sexual harassment, or true threats (“I will hurt you if I see you in the dining room again”). At the same time, the First Amendment protects a wide range of viewpoints, including those that many consider, or that just are, offensive, hurtful, insulting, or humiliating.
If someone on campus says, “Capitalism is racism,” or “Israel should never have been created,” or “Democrats are communists,” or “January 6, 2021 should be…