If you're looking for an honest answer, I believe a large part of it is the diseases we vaccinate for are no longer in our collective memory. A quick Google images search of kids in an iron lung, things of that nature. I don't think I know anyone who knew anyone with polio. Or whooping cough. Or typhoid, Spanish flu, yellow fever, measles, take your pick. So we as a people forget the horrors of loving through those goggle pics. We as people tend to forget it goes a bit beyond the sniffles and a fever. That we're talking about diseases that'll kill you as effectively as a bullet from a gun. Only much more painfully.
Just to throw it out there, it's not just the nut jobs who have large families. Some are just regular people who just really don't like lame sex.
ETA: then there's Google U. Your can spend a few minutes on anti vaxxer sites and scare the shit out of yourself. Much like Fox News, a steady diet of shady quasi correlation presented by some celebrity without a clear understanding of what it is the research actually says and how to correctly interpret it can lead to, well to be brutally honest, lead to children and adults dying of easily preventable diseases.