I don't think that religion plays too much into the vaccine thing (at least not conventional muslim/christian/jewish religion). Maybe new-agey religions, same people who believe in the Indigo Children. I think people who don't "believe" in vaccines are just undereducated in science and many who have kids with problems feel the need to blame something; it is hard to accept that something might just suck.
People have difficultly understanding that correlation is not necessarily causation. Some of the nurses I work with absolutely refuse to get a flu vaccine because it 'causes the flu', and these people are medically trained! It shows a lack of our educational system. If my fellow nurses don't get it, what chance does the lay population have?? A couple of them have autistic kids and still wonder if the vaccines may have been the cause......I've brought in literature to assuage their guilty feelings, but they are not 100% convinced.
I once saw on Discovery channel (or was that National Geographic) a documentary about polio vaccine being refused in a rural part of Egypt (or anyway an Islamic country) because the men (of course) think it causes infertility. Or was it Pakistan. I don't remember, but I'm sure it was a Muslim country. Countryside. I remember feeling angry and frustrated because I have a sister who was stricken with polio when she was a year old (in 1966, before the vaccine was available in our part of the world) and sometime in the mid-90s(?), some American mothers started blaming vaccines for their children's autism. If this turns out to have any truth in it it will be very difficult for me to change my mind about Immunization---which is "Immunization is the single greatest contribution of Western Medicine to the cause of human progress." And the fact that I'm an atheist makes the prospect of Religion tainting vaccination with Luciferine intentions a loathsome specter. But so far nothing of the sort looms in the horizon. I think. Do keep us posted.
Anti-vaxers keep saying that they have proof that vaccines cause autism, yet those 'proofs' have been refuted over and over ad nauseum by science. Meanwhile, monies spent tamping down the hysteria caused by ignorance is sucking funds from real research to discover the cause and more importantly, effective treatment of autism spectrum disorders. Meanwhile, people like me get to take care of infants made extremely ill and even dying from these once rare childhood diseases.
I think that people who are fanatical about anything are more susceptible to believe non-nonsensical notions. Of course, this doesn't apply to everyone, but when someone believes in fantasy and the supernatural, I think they are more willing to buy into mainstream/popular ideas with less skepticism. It has a lot to do with followership, and religion is all about the sheep following the shepard. So, I think that religion plays an indirect role in the sense that people love to hear fanatical celebrities like Jenny McCarthy and Jim Carry drone on about how bad vaccines are for children. It's the blissfully blind following the blind (I realize that this may great offense to the visually impaired to be compared to McCarthy; for this I am sorry)