The symptoms of autism in very young babies are extremely subtle and most parents do not recognize them. For that matter, most physicians do not recognize them, either. The symptoms start becoming apparent when children start missing major milestones, such as saying their first words, etc.
What parents may interpret as just a quirk of their child may, in fact, be an early symptom of autism.
Autism has nothing to do with vaccines, but it really feeds into the anti-vaxxers' efforts to stop parents from vaccinating their children. Keep in mind that anti-vaxxer leaders are trying to stop population growth, and believe that causing more children to die of preventable diseases will achieve that goal. They won't tell you that they don't want you to vaccinate your kid because they want your kid to die--instead they use lies to try to fear you into refusing to vaccinate. They have much similarity to the global warmists who see "global warming" as a tool to impose socialist dictatorship on us, since we've rejected all of their attempts to get us to accept it at face value.
Fear mongering at its worst. I would imagine the lawyers are profiting greatly too from all the lawsuits.