Oats don’t contain gluten (the protein found in wheat, barley, and rye), but they do contain a protein called avenin that some people with a gluten intolerance will react to similarly, which contributes to confusion on the issue. Natural content aside, commercial oats are grown and processed alongside gluten-containing grains and are contaminated with gluten as a result. If this amount wasn’t enough to cause a reaction, there would be no need for those of us with gluten-sensitivity to spend more money buying the kind that are grown and processed in isolation. I have definitely had strong reactions to “regular” commercial oatmeal.
I presume you are asking about this in the context of oat bran and are already aware that oats (as oats) are not part of the strict diet.