Dr. Parker left this comment under his post on Safeminds. I can’t link to it directly, so I’ve placed it here for your convenience, with a link back to his post.

William Parker
The study that came out recently (http://www.ncbi.nlm.nih.gov/pubmed/26688372) supports a strong suspicion of mine: acetaminophen exposure to infants/babies/young children might be MUCH more dangerous than acetaminophen exposure to pregnant mothers. The effect on pregnant mothers is real, but in the grand scheme of things, it’s not “very much.”
It would be unwise, obviously, to needlessly incur even a small increased risk of autism for any reason. However, the increased risk of autism following exposure during pregnancy is actually a little less than 2-fold, and it’s only for one type of autism that accounts for only about 25% of total cases. This is not responsible for the great disaster that we think may be unfolding. It’s certainly something to be avoided, but my long-held suspicion is that exposure to the baby is far, far worse. I hypothesize that this has to do, in part, with the known fact that the baby’s liver is not able to process the drug nearly as well as an adult liver. Thus, the baby’s ability to handle other toxic burdens is greatly compromised, as described in the original article.
This idea of enhanced danger to the baby but not the fetus also agrees well with some of the observations described in the article. In other words, although acetaminophen exposure during pregnancy still holds some danger, the mother’s liver probably protects the fetus, for the most part. So, it’s quite possible that the risk of autism when treating babies with acetaminophen is literally a hundred-fold greater than the risk of exposure to a pregnant mother.
I am currently working on a manuscript explaining this issue, and I hope that a prospective experiment involving “acetaminophen withdrawal” in the neonate/pediatric population at a major medical center will soon be conducted. Such an experiment will be required to test the idea, I would imagine.