I'll drop my two cents here. As preface, I'm a CHHC (Cert Holistic Health Pract) and researcher.
The gluten in wheat can damage the vili in the intestinal wall. These villi absorb nutrients, putting them directly into the blood stream as well as manufacture vitamins themselves.
Regardless of whether you get celiac symptoms or not gluten can damage your villi to some degree, even so, wheat can be a non issue - depending on the health of your digestive tract and overall consumption.
A journal study I read (can't remember the source), came to the finding that low levels of vitamin C can contribute to gluten intolerance. Side note, the vitamin C is stores is often just asorbic acid, which is just one element that makes up vitamin C in an orange per se and is often created in a lab synthetically. Alama C is a better, natural source for vitamin C.
A lot of people have sensitivity to other grain proteins that are not well known or tested for like lectin. So you might be buying gluten free when for an individual, lectin could be the problem.
You can have sensitivity or immune reactions that are not anaphylactic or cause digestive discomfort. This usually comes from having a degraded digestive tract where you actually have holes allowing certain food particles into the blood stream. When this happens your body goes into leukocytosis where the body tags/attacks that food every time you eat it, but you may not get symptoms. All the while this food is causing your immune system to work harder and go into attack mode.....wheat is one of those foods that can damage/puncture the actual lining of the intestines, causing these little holes.
I'm not saying don't eat wheat, or gluten. Just do most everything in moderation and slow down enough where you can actually LISTEN to your body.
Side note: Much of the upswing in autoimmune diseases over the past 200 years has more to do with what is lacking from the human organism than what we put into it. Moises Velasquez-Manoff explains this well in "An Epidemic of Absence."
Yours in health