Short answer: yes!
Longer answer: dairy is a cross-reactive food, meaning it doesn’t contain gluten, but your body may respond as though you ingested gluten if you are sensitive to the gliadin protein.
This can be extremely problematic if you rely upon yogurt for your probiotic fix. Avoid cow’s milk yogurt, opting for sheep or goat milk yogurt instead. If choosing cow’s milk products, buy grass-fed, grass-finished products. You can also try a lactose-free product and see if you can tolerate that.
“Patients with coeliac disease (CD) on a gluten-free diet may still have gastrointestinal symptoms. On clinical grounds cow’s milk (CM) protein sensitivity may be suspected…A mucosal inflammatory response similar to that elicited by gluten was produced by CM protein in about 50% of the patients with coeliac disease. Casein, in particular, seems to be involved in this reaction.” – See more at:https://www.glutenfreesociety.org/is-dairy-sabotaging-your-gluten-free-healing/inf_contact_key=c617164b06065d7eb77ca3cefde20025402b0acfe05a272e7405fce049acfa26#sthash.Q67ZC1Nd.dpuf
Read more at https://www.glutenfreesociety.org/is-dairy-sabotaging-your-gluten-free-healing/#PIH6SBruq8YfjUmt.99
Other cross-reactive foods are chocolate, coffee, yeast, corn, amaranth, buckwheat and barley.