I don't have studies off the top of my head, but i do know that there are multiple studies done on the affects of testosterone and autism. And testosterone is definitely a factor in acne. So, while i don't think ASD and acne necessarily have to go together, it seems reasonable that they might due to the common factor of testosterone.
I had very severe acne at about age 12-15; got somewhat better by late teens/early 20's. Now in my 30's, i have the occasional pimple but nothing major. My poor daughter started with it at age 10 or so; it is still going strong. She has tourette Syndrome and one of her tics is to pick at her skin. This makes it worse, of course. She does not want to do meds for the acne so i have not pushed her to take them. We have found some face washes that improve it somewhat, although no cure-alls. My oldest son also suffers from acne but his did not come on at such a young age as my daughter's. Not as severe either. He has had eczema and psoriasis periodically since he was a toddler as well.
We already do a gluten free diet and make a lot of our own food at home, so dietary approach is probably covered. We have found that keeping skin clean and not picking at it are our best preventions. But mine improved and i am a bit hesitant to try the strong stuff on them unless we have no other choice. At this point, i think we will just wait it out. Hopefully once teenage hormones calm down, so will the acne.
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"Them that don't know him don't like him,
and them that do sometimes don't know how to take him;
He ain't wrong, he's just different,
and his pride won't let him
do things to make you think he's right."
-Ed Bruce