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.
No, those delusions should be rebutted, so that when others arrive at a similar hypothesis, they learn where they went wrong.
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?”