Speech act theory points out that the status of the speaker affects whether or not a speech becomes action / actionable. E.g. if a minister (in the right circumstances) says “I now pronounce you husband and wife,” the utterance creates a legally binding union, but if a plumber (in the same circumstances) makes the identical statement, the words have no impact.
It seems to me that when people who align themselves with Nazi or fascist philosophy / history make anti-Semitic remarks, those statements most certainly become “fighting words” — not just because they incite a hypothetical audience to fight but because they carry the weight of someone who is willing to fight in order to fulfill the threat of the words. Much as if a redneck uses the n-word, that speech act is more intimidating than if an African American uses the n-word.
And if a presidential candidate who cozies up with fascists / alt-right extremists uses anti-Semitic imagery in his tweets / campaign advertising….