The only legitimate reason these anti-vaccine folks have that they can cite was a single paper, written by Andrew Wakefield and his group, published in February of 1998, in the British medical journal "The Lancet". So what did the paper actually say?
The paper is a study of twelve children with developmental disorders (i.e. autism). Eight of the parents claim that the symptoms started after the MMR vaccination. Studies show some sort of gastrointestinal problem in addition to the developmental problems seem to be in common among the children. However, the paper did NOT prove any sort of association between MMR vaccine and autism. What was its conclusion? Without the medical-ese, what it says is:
These kids, previously normal, now have digestive problems and autism, which seems to be triggered by something in the environment.Absolutely NO mention of the vaccine at all was in the paper's conclusion.
The author, Andrew Wakefield, in a press conference before publishing the paper, stated that he believe it may be prudent to use single vaccines instead of the triple-combination MMR vaccine until it can be proven that there really is no link between the MMR vaccine and autism, even though there was no evidence that single vaccines will avoid triggering autism. This is his personal opinion, and was NOT in the research paper.