Volokh is on the case:
I keep hearing about a supposed “hate speech” exception to the First Amendment, or statements such as, “This isn’t free speech, it’s hate speech,” or “When does free speech stop and hate speech begin?” But there is no hate speech exception to the First Amendment. Hateful ideas (whatever exactly that might mean) are just as protected under the First Amendment as other ideas. One is as free to condemn Islam — or Muslims, or Jews, or blacks, or whites, or illegal aliens, or native-born citizens — as one is to condemn capitalism or Socialism or Democrats or Republicans.[…]
Finally, “hostile environment harassment law” has sometimes been read as applying civil liability — or administrative discipline by universities — to allegedly bigoted speech in workplaces, universities, and places of public accommodation. There is a hot debate on whether those restrictions are indeed constitutional; they have generally been held unconstitutional when applied to universities, but decisions are mixed as to civil liability based on speech that creates hostile environments in workplaces (see the pages linked to at this site for more information on the subject). But even when those restrictions have been upheld, they have been justified precisely on the rationale that they do not criminalize speech (or otherwise punish it) in society at large, but only apply to particular contexts, such as workplaces. None of them represent a “hate speech” exception, nor have they been defined in terms of “hate speech.”
For this very reason, “hate speech” also doesn’t have any fixed legal meaning under U.S. law. U.S. law has just never had occasion to define “hate speech” — any more than it has had occasion to define rudeness, evil ideas, unpatriotic speech, or any other kind of speech that people might condemn but that does not constitute a legally relevant category.