Anti-vaccination advocacy exists because some kids do get problems from vaccines. I'm not an anti-vaxxer but it's an inherent feature of how vaccines work that a very small percentage of kids will have some serious things happen as a result of being vaccinated. When you have a big population and the Internet, this small percentage of parents will logically come together to cope with their problems. The fact that those people exist and they can talk about it is evidence that our system is working, not that it isn't.
That is a very charitable portrait of the anti-vaccination movement. No, they aren't parents of vaccine-allergic children banding together "to cope with their problems". They are people spreading serious misinformation about vaccines, advocating that they are risky and best forgone, and causing real damage by doing so. I think silencing these people is wrong, but that doesn't change the fact that their speech is clearly making the world a worse place.
