Just came back and a bit surprised at the downvotes... but that's ok.
I don't know a huge amount about the connection, but I know many autistic kids have GI issues (loose stools) and this has many families considering diet changes as a treatment, so to speak.
If you look through my history, you will see that I actually donate stool for stool transplants. My understanding of the connection (or what the hypothesis is) is that the flora of children doesn't adjust the same in autistic kids as it does in others. We naturally have a level of Clostridia bugs in our guts when we are born and they typically taper off at around 10 months or so. It's believed that in some kids, it doesn't taper off and continues to grow in their gut. As we know, Clostridia bacteria are great at producing toxins (botulism, c. diff toxin, GAS gangrene) and it's believed the Clostridia that are in the babies guts are producing neurotoxins that produce these autism symptoms. We've completed transplants on a few autistic kids with mixed results (younger kids seem to do better than older kids, the thinking is that the older you get, the more damage the neurotoxins have done).
As many have pointed out, autism is still such a new diagnosis, and it's truly a spectrum of symptoms, but also a spectrum of causes. Therefore a stool transplant might not work for every child.
There are many studies about autism and GI issues over several years. Parents of ASD children take heat for trying various things to help their kids, including diets. There are several diets that have helped some kids, but as you wrote autism is a wide spectrum and no two may react the same.
The biomedical side of autism is often dismissed, and likely misunderstood, which I think explains the downvotes. Spending time with hundreds of children with autism, and you start to hear similar complaints and issues. Many of these kids are sick.
The microbiome of the gut is like the new frontier of medicine. It's currently very en vogue and lot's of interesting research coming out. For example, the link between bacteria population in your gut and obesity.
Diet can drastically alter these populations, and therefore when parents adjust diets (remove gluten, remove dairy etc etc) they are actually adjusting the gut flora.
The microbiome may be new, but treating children with behavioral issues with dietary intervention goes back 100 years (with varying levels of success).
The GFCF diet (and others) seems to get criticized because parental reporting doesn't seem to match scientific studies. But the anecdotal evidence is overwhelming. The Autism Research Institute has surveyed thousands of parents about diet and results, and some of the diets have a high success rate with helping some symptoms.
I don't know a huge amount about the connection, but I know many autistic kids have GI issues (loose stools) and this has many families considering diet changes as a treatment, so to speak.
If you look through my history, you will see that I actually donate stool for stool transplants. My understanding of the connection (or what the hypothesis is) is that the flora of children doesn't adjust the same in autistic kids as it does in others. We naturally have a level of Clostridia bugs in our guts when we are born and they typically taper off at around 10 months or so. It's believed that in some kids, it doesn't taper off and continues to grow in their gut. As we know, Clostridia bacteria are great at producing toxins (botulism, c. diff toxin, GAS gangrene) and it's believed the Clostridia that are in the babies guts are producing neurotoxins that produce these autism symptoms. We've completed transplants on a few autistic kids with mixed results (younger kids seem to do better than older kids, the thinking is that the older you get, the more damage the neurotoxins have done).
As many have pointed out, autism is still such a new diagnosis, and it's truly a spectrum of symptoms, but also a spectrum of causes. Therefore a stool transplant might not work for every child.