Most wine is considered gluten-free because it is made from grapes, which do not contain gluten. So, for the most part, wine is considered gluten-free and safe to drink. There are a few exceptions however, because certain aspects of the wine-making process can introduce gluten to the final product.o, for the most part, wine is considered gluten-free and safe to drink. There are a few exceptions however, because certain aspects of the wine-making process can introduce gluten to the final product.