Actually cheese doesn’t contain wheat and therefore gluten that people who suffer from celiac have to avoid. This misunderstanding comes from the gluten-free checklist of foods provided by the Associazione Italiana Celiachi on its website. This checklist presents only those products for which industries guarantee the absence of any possible contamination.
It doesn’t necessarily mean that similar, but not included in the list, products contain gluten. It means instead that those companies haven’t provided enough information and guarantees to include products in the checklist. The new regulations on ingredients labelling give enough guarantee: in fact it is compulsory to indicate traces of products that belong to the list of food allergens, and wheat is one of them.