If you take away the right for anti-vaxxers (or climate change deniers in the OP's case) to talk about things on a public platform where they're actively ridiculed, they're going to go underground and create their own communities under the radar.
Say someone goes to that community to try and convince them otherwise and says "hang on, vaccines don't cause autism, here's some research articles", they'll get banned and their post removed, and everyone in the separate community is none the wiser and nobody who uses that community will ever have the chance to be convinced otherwise.
So if you really wanted to stamp out the anti-vaxxers, I guess you'd have to have some kind of monitoring to make sure they don't post anything anywhere about anti-vaxx views. That would need to be done by someone or something powerful, say... Facebook or the government? I don't trust Facebook as their ulterior motive is selling your data for sweet sweet ad money, and I don't trust the government as many governments have shown in the past many times they can't be trusted to regulate speech of citizens (not that I would EVER want to regular speech)
So - why not just let them speak on large public platforms and have them get laughed at?