Why do people with coeliac disease suffer from frequent upper respiratory tract infections?

Gluten sensitivity predisposes to other allergies or sensitivities. 

It is, in part, an immune system disorder, it increases individual’s risk of developing autoimmune disorders and even though it begins in the small intestine, it affects entire body, including lungs, skin and even the brain.  

Gluten sensitivity can damage the small intestine, its mucus membranes, causing malabsorption of nutrients:  vitamins, minerals. This contributes to a weakened immune system and to slow healing from infections. Kind of similar to mild Cystic Fibrosis that also affects mucus production and makes people more prone to respiratory infections.