I am not an anti-vaxxer but I think we should not silence those who question vaccines, their studies and their effectiveness. By banning vaccine criticism in public domain we essentially ensure that only FDA is responsible for calling a vaccine fake, once they approve we all have to fall in line and not be skeptical about them. This gives too much power to FDA (hence a higher possibility of corruption) and a free pass to pharma companies who might push more and more ineffective vaccines with the help of their friends in FDA and CDC.
Google is pretty good at content recommendation and I am sure if they want they can solve this problem much better by identifying diversity in the vaccine criticism and accordingly give it exposure.