>In the US free-speech does include hate speech.
Only in certain situations and there's established case law to this effect. "Free speech" in the US is not a blanket indemnification:
Fighting words are, as first defined by the Supreme Court (SCOTUS) in Chaplinsky v New Hampshire, 315 U.S. 568 (1942), words which "by their very utterance, inflict injury or tend to incite an immediate breach of the peace. It has been well observed that such utterances are no essential part of any exposition of ideas, and are of such slight social value as a step to truth that any benefit that may be derived from them is clearly outweighed by the social interest in order and morality."
Fighting words are a category of speech that is unprotected by the First Amendment