This[0] appears to be a good explanation of what a "free speech absolutist" is, and it isn't "you have to allow free speech in all settings by everyone"

0. https://www.liberties.eu/en/stories/free-speech-absolutist/4...

In fairness, that explanation also agrees that Musk's extension of "free speech absolutist" extends to apolitical speech and an rights to be heard on social media no matter what corporations might think is inconsistent with his longstanding policy of punishing and trying to silence internal and sometimes external critics of his company...

What's it called when "free speech in all settings [is enjoyed] by everyone"?

I don't think there is a phrase for it, but I can see why it would be a common misunderstanding to think that that is "free speech absolutism." As far as I know, there is no concept that requires a private citizen (A) tolerate another private citizen (B) saying whatever they want on A's property. Maybe some form of anarchy.

Thanks for bouncing the idea around. Sounds like naming such an idea would be a powerful shortcut to reach the root of many free speech discussions. Since I'm not above coining neologisms, "speech anarchy" will be the term I will use going forward.