|"Goonies never say die!"|
Readers are invited to draw their own conclusions on such a correlation. Personally, I'm not yet convinced that meat consumption is the primary driving force behind the increase in cases of autism being diagnosed worldwide outside of any mention of the word 'correlation'.
I am however open to further study on aspects of food or food production potentially being linked to autism in some roundabout way as per areas talking about dioxin exposure through food consumption (see here) or even animal antibiotic use being linked into changing gut microbiota  (open-access) (see here too) bearing in mind my not over-selling the whole gut bacteria bit (see here).
I might also draw your attention to some "fundamental limitations" that the authors include about their hypothesis:
"1. None of the authors is an epidemiologist. Our experience is in different fields, namely comparative psychology (first author) and clinical child psychology (second author).
2. The data presented here do not cover sufficient ground to facilitate the proposal of a precise hypotheses.
3. We did not have enough data to run confirmatory analyses, therefore we have limited ourselves to purely correlational statistics, while providing raw numbers retrieved from the cited sources.
4. It is very likely that the real variable that may definitively explain the observed correlations remains invisible, and what we see is just a surface aspect of the phenomenon."
And speaking of meat, I'll also draw your attention to the recent BBC Horizon programme looking at meat and health by Dr Michael Mosley (see here). Although not the best of Dr Mosley's TV efforts (particularly the 'making sense of the statistics' section and the N=1 experiment) the message seems to be that meat - real meat not the processed stuff - in moderation is probably not going to be particularly harmful to health for those that choose an omnivorous diet. Oh, and fat isn't necessarily the bad guy but those trillions of beasties which inhabit our gut might need some further inspection . If however you want an alternative form of animal protein which has a more environmentally friendly footprint, how about mussels a few times a week?
Some music then and having finally taken the plunge into the wonder that is Spotify, I discovered a bit of a blast from the past: A.M. 180 from Grandaddy. Be prepared for more nuggets in future posts...
 Pisula W. & Pisula E. Autism prevalence and meat consumption - a hypothesis that needs to be tested. Medical Hypotheses. 2014. August 14.
 Forslund K. et al. Country-specific antibiotic use practices impact the human gut resistome. Genome Res. 2013. 23: 1163-1169
 Koeth RA. et al. Intestinal microbiota metabolism of L-carnitine, a nutrient in red meat, promotes atherosclerosis. Nature Medicine. 2013; 19: 576–585.
Wojciech Pisula, & Ewa Pisula (2014). Autism prevalence and meat consumption - a hypothesis that needs to be tested Medical Hypotheses : 10.1016/j.mehy.2014.08.007