as an anarchist, i can explain that none of us support government restrictions on speech, and i would like my enemies to be as loud as possible so i know who to target.

You probably mean so-called libertarians or something. No anarchist I know online or in real life accepts hate speech in their community.

No, I've only heard of libertarianism in the context of America. The people I know call themselves anarchists. I don't have much knowledge about anarchism so I don't know if there's different flavors of it. Like I've heard of anarcho-communism which must be fundamentally quite different. Based on the conversations I've had with them, my own understanding was that the idea would be almost like Laissez-faire, but even more extreme since there's no government at all.

Almost all anarchists around the world would not consider those people anarchists. Anarchism is anti-capitalist. Please see the history https://en.wikipedia.org/wiki/Anarchism

If it's not anarchism then what would you call a completely stateless system that still has a similar free market economy to what we have today? As far as I know, Laissez-faire system still has a state. The group I know is mostly well-off and educated people, not some edgy 16yos. Maybe they've taken anarchism and given their own spin to it. I guess it doesn't really matter. I should have said the "anarchists" I know and some groups I've seen online support absolute free speech.

Most anarchists around the world would say that it's not possible except for mutualists. What you're talking about is what Americans call libertarianism.