No, it’s only that people are using differing definitions of “censorship” and talking past each other.
Content moderation is, in fact, a form of free speech. Twitter (for example) is allowed to choose what they want to host on their website, and what they want not to host on their website. This is free speech – it’s their site, one can’t make them host what one writes. If choosing what to remove from their website is deemed “censorship”, then there’s no contradiction.
Consider that Ben Franklin wouldn't publish libelous or slanderous material submitted to his newspaper - clearly a form of "content moderation." He believed in the right of the people submitting such things to express them and would suggest they try elsewhere, but also believed in his right not to publish those views on his "platform."
I don't think anyone would accuse Ben Franklin of not believing in free speech, so clearly a reasonable person can square the apparent circle. Freedom of speech isn't the only right relevant to speech, and freedom of speech doesn't guarantee a right to speak on all platforms.
Viewing moderation as another form as speech seems reasonable to me, or at least as reasonable as viewing a campaign contribution as a form of speech. Perhaps the actual issue is that "free speech" cannot be a guaranteed right shared by all, but is inherently a rivalrous good.
If content moderation is censorship, then you are arguing that if I ask you to say something out loud and you don't say it, you are censoring me.
We've reach a contradiction, so there must be an error in the chain of reasoning. My money is on "content moderation is a form of free speech" being wrong.