Beer is not gluten free and you need to try gluten-free beers like those listed in our Dairy Products: Milk, half and half, cream, cream cheese, cottage cheese. Most cheese does not have gluten, but it is very important to read labels of all packaged or processed cheese before eating it. Cream cheese is gluten-free. Oct 20, So, just why do some people need to avoid gluten in their diets? Is it really necessary? Unfortunately, yes; some people's bodies are naturally.