Almost every time I hear someone advocate for speech policing, they mention obviously awful speech (e.g. Nazi Germany, Sandy Hook conspiracy theories) as an example. And I agree, that speech sucks, most of us can agree about that because we have hindsight to educate us. In reality, speech is really murky. From what I recall from history classes, "Nazi" ideas like Eugenics weren't Nazi ideas, they were popular at the time everywhere, including in the US. Anti-semitism was not Germany exclusive (and still isn't). When you find yourself inside a society, it becomes very difficult to separate yourself from its collective delusions. In this, it becomes dangerous for a central authority to police speech: how to agree on which speech is acceptable (past the generally abhorrent speech like that mentioned above) is difficult and bound to either be abused in the worst case or best case many mistakes will be made.
Historically, because of the issues mentioned above, I feel against most speech policing in general theoretically. Admittedly, however, I also demographically don't really feel the effects of hate speech, so it's easy for me to take this emotionally distant stance.
The best solution I can come up with here is, especially online, a series of filters: bifurcate platforms like Facebook into a feed where content is moderated, and give users options to opt into unmoderated streams (unmoderated to the extent the law allows).