The increase in autism diagnoses is just maths, combined with the fact that - for the first time in history - the modern world places value on the natural skillsets of a lot of autistic people (pattern recognition and work that can be done in isolation, among other things), which means we're no longer outcasts. No longer being outcasts, and having financial advantages, means that we get to participate in the gene pool far more than in eras gone by.
I know this, because there's documentary evidence of 7 generations of autistic folk in my family, and the ones that presented like me? Completely shunned by society, not allowed an education, and shut away for the embarrassment of their existence. In years gone by, I would've been the village idiot; in the modern world, I have an IQ of 158 and I'm incredibly successful in my field.
We autistics also tend to flock together.
Combine those two things, and the result is making more autistic people than ever before.
Then you have the fact that, because there's massively decreased stigma and more accommodation in society for autistic folk, all of us autistic oldies are seeking an explanation for the struggles we've always had.
Presto! More autistics. Nothing to do with vaccines.
The problem is that, because the general public is proud of the fact that they understand nothing about maths beyond primary school, when everybody knows someone who's diagnosed autistic, they think it's far more prevalent than it actually is. That's distortion of perception versus statistics and probability; one requires knowledge to understand, the other is a hand-wave away.