That would come up against the interpretation of the First Amendment espoused by the Supreme Court in 1969, in the case Brandenburg v. Ohio. Before then, the First Amendment was not interpreted nearly so broadly, and speech regulations at the federal and state levels were common, beginning with the Alien and Sedition Acts soon after the Constitution was ratified.

If/when the Democrats restructure the Supreme Court to have a liberal majority, overturning Brandenburg with a single ruling becomes on the table, and the door is open for hate speech legislation.