It certainly doesn't. It's just that alt rtght absolutely abuses good will and rules to the extreme and systematically hijacks certain phrases.
See Elon Musk's Twitter as a light example (giving in to authoritarian censorship, and skewing content visibility, while constantly touting himself a "Free speech absolutist"), or the_donald from Reddit, which was mostly made of bots, conspiracy theorists and some sane, but malicious people, banning anyone who's even slightly misaligned.
Some people like the previous commenter are then incorrectly shortcutting hijacked slogans to the alt right. Which was their goal to start with - increasing the friction, uncertainty and division.
To elaborate about free speech we want to mantain sensible environment. So we need to give a boot to astroturfing bots and far, far right neonazis. Though as with most things, moderation is the key.
MonsieurHedge