There was a study in a very reputable medical journal in 1998 that opened the argument for vaccines being the primary cause of autism. 2 weeks ago, The Lancet (journal that published the article) retracted it saying that it was based on unsound science and author bias.
Someone's bad science made for a world of fear and anxiety.
In our case, we've had all the vaccinations that the pediatrician recommended. Our reason for doing it? Our pediatrician's kids are all a year older than ours, and he had each of his own kids vaccinated for the same reasons.
Personally, just like with Diabetes, I believe that the reason so many more cases of Aspergers/Autism spectrum disorders are being diagnosed is because we understand the diseases better and have better diagnostic tools.
Look at ADD and ADHD - it was almost unheard of when we were growing-up and now just about anyone with problems focusing is diagnosed.
I'd recommend you visit three websites:
1. American Academy of Pediatrics (aap.org)
2. Centers for Disease Control (cdc.gov)
3. Food and Drug Administration (FDA.gov)
I know you can call directly into the CDC and FDA as a consumer and ask for information. You can also do the same with your County/State Departments of Health.
You should also check with your state to see if your children can attend school without their vaccines completed.
Your pediatrician is only recommending them because they believe the benefits of providing the vaccines outweighs the risks. That doesn't mean that there are no risks involved, it just means that for the general population, it is in favor of benefit. I'd also recommend speaking with an expert in the area of the autoimmunie disorder you recommend (perhaps a geneticist) to see what the likelihood of your children having some of the known side effects is.