From my admittedly limited perspective as a parent of an infant and a preschooler, it seems to me that say… 5-10 years ago, if someone spouted off about being against vaccinations, people just chalked it up to them being a bit of an oddball.
Sometime in 2012 or so, Andrew Wakefield’s research was shown to be fraudulent, and shortly thereafter there have been several outbreaks of diseases such as measles where either the patient zero, or the majority of the afflicted children were unvaccinated.
Also, at about the same time, there’s been a grass-roots effort on the part of non-ignorant parents and media figures to try and educate the public about vaccinations (Penn & Teller, Neil deGrasse Tyson stand out) or if nothing else, show vaccinations as a normal part of infancy/early childhood (believe it or not, the Kardashians are who I’m talking about).
And finally, in the past few years, there’s been a big resurgence in the thought that “Science is cool!”, and vaccinations are fundamentally a scientific thing, so I think that helps as well.
So ultimately, antivaxxers went from being considered a bit eccentric and looking out for their children in their own silly, but harmless way, to being viewed as ignorant, pig-headed fools who are not only endangering their own children, but other children who are either too young to be immunized (< 1 in the case of MMR), or who have weakened immune systems for whatever reason.
This also tracks pretty clearly with my internal thoughts- if someone would have told me they weren’t vaccinating their kids in 2004, I’d have thought this person was definitely a weirdo, and probably pretty rare. I likely wouldn’t have said anything. But I had someone tell me and a buddy that they weren’t vaccinating their daughter in 2011, and my buddy and I proceeded to tell him what an dumbshit he was (exact term!), and how he’s endangering her, and how we thought he’s smarter than that, etc… all stuff we’d have NEVER said in 2004.