I don't know if this applies to anyone here, but some case of what are labeled "schizophrenia" may actually be undiagnosed cases of an illness called Hashimoto's Encephalopathy. It is a rare complication of autoimmune thyroiditis that can lead to all kinds of neuro symptoms as well as psychosis. Most psychiatrists have never even heard of HE and so would never consider checking for it (by testing thyroid antibodies) in a patient labeled schizophrenic.
As with other cases of autoimmune thyroiditis, patients who have HE are at increased risk of a wide variety of other autoimmune diseases- in particular celiac disease.
So, perhaps this is the real reason that "schizophrenics" are at increased risk of celiac- maybe it is those schizophrenics who actually have undiagnosed HE (which is unfortunate, as HE is highly treatable with steroids). I guess only time and more research will answer this question.