The relevant passage doesn't specifically say "hate speech. It's the fighting words / treats section. Here is the relevant passage:
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Fighting Words and True Threats
So-called “fighting words” also lay beyond the pale of First Amendment protection.19 The
“fighting words” doctrine began in Chaplinsky v. New Hampshire, where the Court held that
fighting words, by their very utterance inflict injury or tend to incite an immediate breach of the peace and may be punished consistent with the First Amendment.20 In Chaplinsky, the Court
upheld a statute which prohibited a person from addressing “any offensive, derisive or annoying
word to any other person who is lawfully in any street or other public place,” calling “him by any
offensive or derisive name,” or making “any noise or exclamation in his presence and hearing
with the intent to deride, offend or annoy him, or to prevent him from pursuing his lawful
business or occupation.”21 The state court construed the statute as forbidding only those
expressions that “have a direct tendency to cause acts of violence by the person to whom,
individually, the remark [was] addressed.”22 Given the limited scope of application, the Supreme
Court held that the statute at issue did not proscribe protected expression.23
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Most hate speech falls under this category. For instance, advocation of the murder of a large group of people would obviously be unprotected hate speech.