I would argue that the public doesn't "largely" believe that. The majority of parents get their kids vaccinated.
It is a small fringe of people who believe things like that; just unfortunately these same people are the most likely to catch the disease (and be unable to afford decent treatment).
The really unfortunate thing is they can compromise herd immunity, leading to people who can't be vaccinated or even people who WERE vaccinated getting infected.
I would be much more tolerant of the people who are afraid of vaccines, if it wasn't for the risk of them hurting other people with their decisions.
It is a small fringe of people who believe things like that; just unfortunately these same people are the most likely to catch the disease (and be unable to afford decent treatment).