Earlier quoted context omitted.
Is it? If A says to B, "don't vaccinate your kids", B complies, and then B's child dies of a disease it could have been vaccinated against, you would not say A had any culpability?
Let's keep going, though... there IS a non-zero chance that your kid can die from a vaccine. It is very very rare, and more kids will die from not getting a vaccine than from getting one, but there will exist a parent who can say truthfully that vaccines killed their kid. Can they then argue that a pro-vaccine person killed their kid? Can they sue their doctor? If we allow this line of reasoning, where does it stop?…
I don't disagree with being upset with antivaxxers and thinking they are causing real harm to our society.
However, I think the harm is outweighed by the benefit of allowing people to make whatever arguments they want in public (much like I think the risk of dying from a vaccine is worth it because of the reduced risk of dying from the disease the vaccine is preventing). The alternative is having to set some sort of 'risk threshold', where you aren't allowed to argue for something that increases risk more than x%..... but that gets really complicated, because most of the times you are advocating to increase risk IN RETURN FOR SOMETHING ELSE.
For example, driving a car is EXTREMELY risky (and kills way more people than die from not taking a vaccine). However, most people feel the benefit of auto transport is worth the risk. However, that is very subjective, and it would be difficult to logically and objectively argue against someone who says that risk is not worth it, and we should outlaw cars.... and anyone who advocates driving is responsible for every automobile death.