This is not entirely the same as being celiac. You can still have very small amounts of gluten, whereas someone being celiac should not eat any at all.

We have found that it isn't so much the quantity of gluten, but the quality of the product. For example, a piece of cheap, white bread has bad effects, but a piece of whole grain, organic bread or sourdough is usually fine. This could be fodmaps, but we have tried cutting those without much effect.

Right now, our working theory is contaminants and mimic weeds that make their way into wheat and other cheaper products where as the supply is a bit more controlled in the higher end and organic products. But we are still mostly befuddled.