There’s a lot of interesting observational research on this topic, and in particular I found this paper[1] interesting because it shows a similar link with Tylenol and autism in young infants, but did not find the same effect for ibuprofen, which to me almost rules out fever/infection as the root cause.
There was another paper I saw that even suggested the anti-vaxxer conspiracies may stem from the fact that doctors and parents give Tylenol to their kids to manage the side effect of some vaccines.
Interestingly, there is also a separate body of research[2] that has shown experimentally that acetaminophen causes emotional blunting and reduced empathy in adults - could be related?