Best I can tell, the benefits of vaccination far outweigh the risks. I am pro-vaccination.
That said, I have often felt that, accusing people who are against vaccination of stupidity or scientific illiteracy, is too simplistic and intellectually lazy.
Science as an activity involves proffering hypothesis and running experiments or studies to determine the validity of the hypothesis. Unless one has access to research in the specific area of study and has taken the time to understand and weigh the evidence for and against their position (whatever it may be), it is dishonest for them to claim that their position is scientifically correct.
Most people do not have the access or the time to undertake such research. Nor is it practical or reasonable, for everybody to take such an approach, to the vast number of choices that confronts them during their lifespan. Instead, people often look up to trusted proxies for answers – be it Neil DeGrasse Tyson, FDA , Dr Oz or Dr.Phil. Sometimes these trusted proxies can be wrong. More often, as science progresses evidence mounts to disprove the current scientific consensus. What is believed to be true today may indeed turn out to be wrong.
In such a context, it shouldn’t be unexpected that some percentage of the population is unwilling to accept what is otherwise the current consensus on some specific topic.
I recently stumbled upon two articles that expressed a similar viewpoint.