California AG's Brief Claims "Hate Speech" Is Constitutionally Unprotected

From a brief filed by the California Attorney General's office in Ogilvie v. Gordon, a case dealing with restrictions on personalized license plates (such as exclusions of "racially degrading term[s]"):

There are well-defined and narrowly-limited classes of speech, "the prevention and punishment of which have never been thought to raise any Constitutional problem." Chaplinsky v. N.H., 315 U.S. 568, 571-572 (1942) (emphasizing that certain types of speech are protected by the First Amendment). Obscenity, vulgarity, profanity, hate speech, and fighting words fall outside the scope of the First Amendment's protections. See Brunetti, 139 S. Ct. at 2303 (Roberts, C.J., concurring in part and dissenting in part) (forbidding registration of "obscene, vulgar, or profane marks does not offend the First Amendment"); Brown v. Entertainment Merchants Ass'n, 564 U.S. 786, 791 (2011) (listing instances where the First Amendment does not protect speech); R.A.V. v. City of St. Paul, 505 U.S. 377, 383, 393 (1992) ("fighting words," defamation, and obscenities fall outside the First Amendment).

Actually, nothing in Chief Justice Roberts' separate opinion in Brunetti, or the majority opinions in Brown and R.A.V., says or even suggests that "hate speech" is "outside the scope of the First Amendment's protections." Indeed, R.A.V. holds that selective bans on racist fighting words (as opposed to broader bans on all fighting words, racist or otherwise) are unconstitutional; and Justice Alito's four-Justice opinion in Matal v. Tam, which Roberts joined and on which the Brunetti decision relied, expressly says:

[The idea that the government may restrict] speech expressing ideas that offend … strikes at the heart of the First Amendment. Speech that demeans on the basis of race, ethnicity, gender, religion, age, disability, or any other similar ground is hateful; but the proudest boast of our free speech jurisprudence is that we protect the freedom to express "the thought that we hate."

Justice Kennedy's separate four-Justice opinion in Matal agreed with Alito and Roberts that restrictions on allegedly bigoted speech are unconstitutional. There and elsewhere, the Supreme Court has made clear that there is no "hate speech" exception to the First Amendment.

The California AG's office is of course entitled to argue to the Supreme Court that it should recognize a new First Amendment exception, though I think the Court has been wise to reject this one. (Of course, if such an exception were recognized, then it means that speech could be outright criminalized, and not just excluded from personalized license plates, which is the question involved in the Ogilvie case.) But I can't see how the office can just assert this claim as if it were indeed supported by the opinions that it cites.