More anti-vax hooey?
FYI, that journal article that you referenced actually discounts vaccines as a contributor to autism. The article specifically mentions acetaminophen as a potential contributing cause—although it is not convincing. For one thing, it mentions adverse effects of acetaminophen in animals without mentioning doses.
The etiology of autism spectrum disorder suggests a strong genetic component modulated by many genes. In the case of most genetic conditions, having the genes is necessary for the condition to occur, but do not cause it. The condition actually happens because of an environmental factor that would not affect a person without the genes, but strongly affect a person who does have the genes. For example, some children are born with a defective DNA repair enzyme which causes them to develop permanent skin lesions upon exposure to UV light. But if they are never exposed to UV light, their skin will remain intact.
In the case of autism, the genetic contribution is complex and will take many more years of study to figure out. If environmental factors are involved, they likely act early in fetal development.
Note a rather common genetic anomaly that cases the heavy metal clearing pathway of the liver to operate at 10% of normal is suspected to cause hyper sensitivity to mercury and may be the cause of thimerosal poisoning linked to autism.