This is a mentally damaged individual. I'd like to see elaboration on what "people like you" entails. But I would guess it's anyone who makes them feel angry or stupid.
Freedom of speech is also a principle. Generally speaking, the operator of a forum should strongly value that principle, and refuse to censor any natural person's speech.
You are correct that an individual's right of free speech isn't infringed by by private censorship. The right to free speech is infringed by incarceration or other official sanctions. You absolutely should have the right to free speech on that private platform, as you should not be jailed for your statements made on it.
Note: not all forms of expression qualify as speech. CP and death threats, for example, are forms of violence, not forms of speech.
The operator of a forum should absolutely remove delusions when they're aware of them, even if they are not CSAM or overt calls to violence. There is nothing of value lost by excluding Nazis from "just asking questions," on the contrary, society is better for it.
Why are people arriving at delusions that are in actual conflict with reality? Because there are mountains of content debunking all that shit. There are already hundreds or thousands of rebuttals. Why do delusions persist? Is it perhaps that people spreading them are successfully able to radicalize others by "just asking questions?"
They are getting banned from public spaces any time they bring them up. So instead of learning why they are wrong, they are instead sent off to find similarly delusional people. Censoring (moderating) feeds the echo chamber.
That's just not a realistic perspective of what is happening. People are not coming up with these ideas in a vacuum, nor does simply giving them the actual facts cause them to reevaluate their positions.
There are still people out there trying to pretend like the Holocaust did not happen. This is one of history's most well-documented atrocities. Lack of information is not a problem here. People are deciding to believe this delusion after they are radicalized by bad faith actors on social media.
Private forums can regulate whatever they want. If you don't like it, find another one.
However, I do think this breaks down when a few outlets dominate. YouTube, Facebook, and Xhitter are all examples. Federated platforms, like Lemmy, are the solution.