In the context of US constitutional law, yes. But freedom of speech can have a wider meaning in moral philosophy. What someone might mean when they speak of the idea will vary.
Anyway, I don’t think anyone has an obligation to listen to or host content they find offensive or harmful, but in the context of a public forum that hosts a wide range of non-curated content and discourse, removing content or banning people just because it is critical of you or you disagree with it may be morally wrong. Especially when there are clearly outlined rules and the content does not clearly violate those rules. This happens frequently on this instance (and others, but this seems to be the main offender among the big instances currently).
That'll always come down to the moderation team and their views of content, and it'll always be a thing in online forums. I can still remember the, ahem, other place, and their mods on a power trip were legendary for stifling conversation points they disagreed with. Same thing happened on Digg before that.
It is worth remembering: any law reflects the moral right to free expression. There are limits - there are always limits - but you are correct to have some expectations of leeway, anywhere you go.
"If you... Have your show cancelled, get banned from an internet community"... That's censorship and it's a direct violation of 1st Amendment free speech rights. Don't believe it? Look up the case where the ACLU actually defended the KKKs right to free speech and they also defended other radical and reactionary groups back when the Constitution was still respected and adhered to. Then you'll know what free speech really is. Dictatorships can't exist without censorship.