Real feta cheese, like most real cheeses, is gluten free. However, processed cheeses, such as products labeled "cheese food" or cheeses that contain additives, may not be gluten free.
Gluten is an ingredient prevalent in meat, barley and rye. Since most flours are derived from one or more of these ingredients, most flours also contain gluten. Cheese is made from milk and allowed to age for a certain amount of time while bacteria digests the lactose in the milk and turns it to cheese. Non-processed dairy products, grains, meat and nuts are friendly to those who either desire or must maintain a gluten-free diet.