It is a very thought provoking question and one that deserves discussion so I look forward to the comments that will surely follow the post. I personally think that they are both based on the same basic problem which is misinformation.
A comment prior to my own on the site brought up a very valid idea:
"Fundamentalists are inherently more dangerous since they promote blind faith over evidence. Anti-vaxxers at least attempt to follow evidence, albeit very poorly, and still see the value of evidence. A fundamentalist will believe in spite of evidence and sees this as a virtue."This is kind of an eye opener and I totally agree with the poster. Religion is not only a source of misinformation like Anti-Vax propaganda, it is also a terrible alteration of logic and morality. Morality itself is of course subjective but that is a post for another day.
Anti-vaxers actually do value the idea of evidence, proof and statistics, however much they misinterpret them, whereas religious fundamentalists simply ignore logic and look at evidence as if it were blasphemy.
"Reason is the greatest enemy that faith has; it never comes to the aid of spiritual things, but - more frequently than not - struggles against the divine Word, treating with contempt all that emanates from God" - Martin LutherThis quote is revealing of the true nature of the religious world view. It seems like common sense to be reasonable when having a discussion and coming to a conclusion, however the religious mindset is to literally ignore reason and trust in faith, blindly and without any proof aside from anecdotes.