I have multiple automimmune disorders. The worst of which is psoriatic arthritis. I don't know if there is a connection between them and my autism or not but I do know they interact badly with each other. My autism makes it so I don't realize soon enough how much pain I am in and carry on walking or using my joints making my arthritis crippling instead of just severe. It's a nastly reality.
If autism is associated with autoimmune diseases, it's unlikely to be due to one causing the other.
Much more likely is a gene expressed both in the brain and some immune-related cells, which when mutated changes development in both areas.
Just like with cystic fibrosis, the digestive issues don't cause the respiratory issues or vice versa, it's just that the same gene affects lung development and pancreatic development. (I'm not trying to say autism is like cystic fibrosis, just that CF is a genetic condition affecting multiple organ systems.)
I can't do the correct science from my head, but the digestive issues do cause immune problems. Genetic low digestive enzyme production, body can't digest, protection on lining of digestive system gone, peptides in bloodstream, immune response to this (food intolerance), also candida (no joke, I'm still trying to get rid of it) needs full immune system's attention, viruses and bacteria take over, also no enzymes to break down histamine from food, so asthma, So just that one autistic trait can make a pretty good mess. Maybe I'm one of the few older ones here, but my immune system is pretty shot.
I have two: rheumatoid arthritis and Sjogren's syndrom. I don't know if there's any connection to the Asperger's...