There’s some good and bad news. The bad news: the traditional Old Fashioned Oats are not gluten-free. While they do not contain any gluten ingredients, Quakers themselves have told celiacs and gluten intolerants to avoid this product.
Much like oats, oatmeal is often not gluten-free, unless specifically carrying a gluten-free label. This is because of potential cross contact throughout the process from growing the oats, to hitting the shelves.