There is as much evidence linking diet soda to autism as there is vaccines. By this, I mean there is none. Being a parent is hard and I know you want to protect your kid, but part of protecting your kid is protecting them from preventable diseases. I also know that you wouldn't like it if your kid got something because another kid wasn't protected.
Diet soda doesn't cause autism, nor do vaccinations. The difference is that a vaccine will actually save your kid's life.
Get your kids vaccinated!