Mostly only illegal content should be removed.
And that's how you end up with a Nazi bar. Sure a swastica tattoo isn't illegal; nor is saying death to jews. But most people don't want to drink in that environment so if you don't kick (censor) the nazi's out then your business will not get non-nazi patronage (and maybe go under). The "free market" has determined that censorship is desired.
In the digital space, filters work just fine. Your messages will live in the same database as the Nazi's, but you can be completely isolated from seeing them if you set up your filters accordingly.