I think there IS a lot of conflicting information out there, and I'm not sure the "proper" conclusions are as clear as we all would like them to be. You will find that the AS community by and large thinks any worry about vaccines is bunk, and has been discredited. Still ... it's not impossible that some children have had adverse reactions that make their spectrum symptoms appear worse, or mimic spectrum symptoms. I'm not convinced that all the anecdotal stories come completely from myth; someone did feel they experienced these things, and the question becomes why.
I trust the CDC more than the opposite flank, because at least those are people who really, truly understand the science and won't personally profit from the positions they take. A LOT of money has been made by the anti-vaccine camp. Big pharma isn't the only with a profit agenda.
What to do?
Rule out all the known risk indicators (allergies to ingredients, mitocondrial disorders, etc), then do the right thing by society and vaccinate. Go ahead and slow down the schedule if you feel that is appropriate (many countries go much slower than we do), but accept that the cost benefit analysis for society as a whole falls squarely into, "vaccinate." It isn't risk free, it never was, but the equation only works to protect everyone from horrid diseases if everyone takes part.
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Mom to an amazing young adult AS son, plus an also amazing non-AS daughter. Most likely part of the "Broader Autism Phenotype" (some traits).