I often hear people arguing that some speech is unprotected under current First Amendment law because it's "hate speech," or asking "Is [X] free speech or is it hate speech?" That, it seems to me, is a mistake.
"Hate speech" is not a legal term of art under U.S. law, nor an exception from First Amendment protection. Some of what some label "hate speech" may, depending on the circumstances, fall within the generally quite narrow exceptions for fighting words, threats, incitement, or certain kinds of false statements of fact. But if one thinks a particular scenario or incident is unprotected on those grounds, one needs to mention the specific exception, and explain how the speech fits within that exception.
Of course, one could argue (though that's not what the people I'm referring to above are doing) that the Supreme Court should create a new "hate speech" exception from First Amendment protection -- that the speech is currently protected, but ought to become unprotected. But then one needs to explain precisely how one would define this new exception, since "hate speech" doesn't have a clear and well-accepted definition. And of course one should then respond to the foreseeable arguments about why this exception would be unacceptably vague or broad.
Simply asserting that some speech is unprotected under current First Amendment law because it's "hate speech" doesn't demonstrate much of anything -- except that it demonstrates to those readers who are familiar with First Amendment law that the speaker isn't making a sound First Amendment argument.