The anti vaccination movement was strong before AI. I would correlate it more with rise of social networks than AI. It'd be interesting if there was a data based graph but I wonder what the source data would look like - antivax is externally imposed label, most people in the community will describe themselves as vaccine skeptical or hesitant, for a while they even used the term woke (entirely different meaning than Conservatives call people with functioning empathy glands).
While most consumer LLMs are supportive and syncopatic, their default trained behaviour is relatively scientific based. Of course a few prompts and settings will "fix" that but I don't think AI is required for the echo chamber and incubator - I think tiktok and Facebook etc provided that breeding ground.
(I also don't subscribe to radical theories on planned depopulation but willing to hear thoughts on contrary :)