I'm studying some of these issues in both autism and Ehlers-Danlos Syndrome (EDS)/Hypermobility Spectrum Disorder (HSD), which seem to overlap each other somewhat. Overall, these two overlapping populations report a lot of symptoms that are indicative of 1) immune dysfunction (autoimmunity, general inflammation, mast cell activation disorders) and 2) dysautonomias. "Dysautonomia" means that there is dysfunction of the autonomic nervous system. In these conditions, there tends to be an overactivation of the sympathetic branch ("fight and flight"), which often causes GI symptoms. The other branch of the autonomic nervous system is the parasympathetic branch, which is the "rest and digest" branch. So you can imagine why one might experience constipation when your sympathetic nervous system is overactive. Reflux in this context can also be a subtle sign of gastroparesis, which means that the stomach is emptying too slowly into the intestines and so the stomach tries to accommodate by producing more stomach acid. The most extreme form can result in vomiting, but there is a spectrum of severity and can be highly under-recognized by doctors.
Common symptoms of dysautonomia are (but are DEFINITELY not limited to):
-Difficulty standing still (this is intended in the "discomfort" sense, not the hyperactive sense)
-Fatigue
-Lightheadedness
-Nausea and other GI symptoms
-Brain fog or mental clouding
-Palpitations or chest discomfort (also includes high heart rate or changes to blood pressure)
-Shortness of breath or difficulty breathing (may be confused with asthma but doesn't usually respond to asthma meds as well)
Immune dysfunction can also cause a lot of GI problems as you can probably imagine. For instance, acid reflux can also result because of high histamine levels related to general inflammation. Histamine in turn triggers higher production levels of stomach acid. Also, one might be sensitive to various foods, either as an allergic or non-allergic reaction, which can obviously trigger dysfunction and general unhappiness in the GI tract.
So, anywho. Takehome message is: Yes, there's lot of GI issues associated with autism and there are several underlying conditions (immune disorder, dysautonomia) that are often at the root of those issues. If you're interested in reading more, I highly recommend the literature on dysautonomias (the diagnosis "postural orthostatic intolerance syndrome" or POTS has a lot of relevant literature) and immune disorders like mast cell activation syndrome (MCAS). While these are both diagnostic extremes of this continuum, they may have some info that is nevertheless applicable to your situation and could be useful. Hope this helps! 
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