I think it's more likely correlation than cause-and-effect.
I have a friend with 2 kids with celiac, one was born vaginally, the other was born via c-section. They both also have type 1 diabetes. Type 1 diabetes and celiac are both auto-immune disorders and they're both carried on the same gene.
I'm wondering if there's a link between celiac and all other auto-immune disorders. And somehow gluten is causing it all. Wish I had some research grant money.
I have 3 kids, 2 with gluten intolerance (DS and DD2, not celiac), and one of those was born vaginally (DS) and one born via c-section (DD2). We just got DS stool tested and he's the one who's missing the good bacteria, so who knows (I have yet to get her stool tested, but it will be interesting to see).