The vast majority of parents who refuse vaccinations do that absolutely NOT because of religious beliefs.
vaccines are NOT BENIGN products - it a foreign protein and it can cause a lot of harm ( not talking autism here).
American vaccination schedule is so overloaded that being a responsible parent one SHOULD refuse it and work out their own, individual schedule - but that requires a lot of personal reading and learning on the issue.
I say the most ridiculous one is the chicken pox vaccine. News flash: you WANT your children to get chicken pox! Ideally, between ages six and ten. It's no big deal for a child, and after getting it, they are immune. (I was seven.) The vaccine is less effective (I recall, only about 65%), and an adult getting chicken pox can be in serious trouble! (My grandmother never had it, and her doctor told her that it could kill her!)