There is an entire Behind the Bastards series on people who shilled the anti-vax rhetoric.
Robert makes the point that for the anti-vax crowd, it's the idea that "you are a bad parent and that's why your kids got autistic" is worse than "vaccines gave your kids autism".
It's even worse when you add genetics to the mix because now parents have to believe something made their kids this way instead of something they had no control into.
The absolutely wild thing is that anti-vax used to be a largely liberal stance but with the added conspiracy theories, it swung over to the right.
So, TL;DR: parents are assholes who don't want to face reality that their child is not what they wanted them to be and would rather not have the burden of raising them and blame something else.