A lot of the anti-vaxers are just convinced that the statistics about measles deaths are made up & that it's just big pharma's way of pushing poison in to people to make everyone autistic. I still encounter people who believe vaccines cause autism even after that was debunked. I linked to the article showing it was a false study to begin w/ & one girl's response was about how there are more cases of autism now so it must be vaccines. I had to point out there are many other factors: Higher populations, advancements in technology, people having children at older ages, reclassification & expansion of the autism spectrum (which is a huge one), & more understanding/knowledge to diagnose. I also think that there are some overdiagnosis cases where kids who are shy at the doctor's office & who were put in front of the TV or left to play video games instead of interacting with other humans come off as socially awkward & get labeled as autistic. I knew a kid who's mother is very neglectful & rarely interacts with the kid except to hit him or scream at him. For the first few years of his life, his mother put him in a little seat in front of the TV w/ a bottle from 7am to noon. Then she'd refill the bottle (when he got older it would be juice in a sippy cup & some dry cereal poured out on the tray) & go back to sleep & leave him there to watch TV for several more hours. Then she wondered why he couldn't talk right & didn't know how to behave around people.
One of the really sad things to me, is that people would rather risk their kids dying than supposedly developing autism (nevermind that, barring traumatic brain injury, people don't develop autism-- it starts at birth because their brains are different).