Well this is a great question. I tell my patients to avoid any gluten on their skin. However, the answer depends up where your focus is.
If your focus is only on gut damage (that is celiac disease), then the tiny amounts of gluten in these skin products is trivial and not enough to cause intestinal damage.
But, if your focus is on the person and symptoms, then gluten on the skin often causes itch and irritability. For example, people complain of itchy hair if using a gluten-containing shampoo. Children using play-dough can develop a contact rash and become irritable. Swallowing gluten in lipstick causes some people a sore tummy.
So what do I do? Well, I recommend gluten-free cosmetics and topical medications. This is what we state in our book “Going gluten-free: how to get started”