We already know vaccines don't cause autism. The antivaxxers yell loud and long, but their evidence is anecdotal and doesn't hold up to scrutiny. But because the forces of antiscience are so vocal, we need to keep restating the obvious.
So here's more force behind the statement: an Italian study shows that thimerosal has essentially no effect on brain function in children who got a whooping cough vaccine.
They didn't, above what would be expected from chance variations. Even better, the study was randomized in such a way that outside factors like environment wouldn't play a role, so antivaxxers cannot say it was something else that may be affecting these results.
Now let's be clear: thimerosal has been known scientifically not to have any link to brain disorders for years (link goes to a Word doc), and the Measles/Mumps/Rubella (MMR) vaccine never contained thimerosal anyway. Antivaxxers wrongly targeted thimerosal as a health risk, and thimerosal was removed from vaccines in 2001, but no reduction in autism spectrum disorder diagnoses occurred. In other words, thimerosal is not linked with autism.
Antivaxxers, not willing to let something like evidence sway them, turned instead to vaccines themselves, even though many studies have been made showing vaccines in general have no link to autism. Still, because this group is vocal and has larger-than-life spokesmen (and because it's very easy to sway the media and public opinion when talking about sick kids, especially because it's so easy to confuse correlation with causation), antivaxxers still have influence in this country. That's one reason why we're seeing outbreaks of preventable diseases.
Don't expect any of this to slow them down; antivaxxers tend to be impervious to evidence-based arguments. As with creationism, quack medicine, and all the other antiscience forces, all we can do is continue to show the public the truth, keep making ourselves heard, and make sure that when nonsense is presented as fact -- especially when our children's health is concerned -- we do not tire. Lives are literally at risk.