While there is not a lot of evidence that exposure from your skin products will cause problems, there is no reason not to avoid wheat in your skin products. Wheat proteins don't add much benefit to the function of skin products so avoid it where you can.
Incidentally, where do you learn about what you can safely eat and be exposed to with this allergy?
Thanks for the feedback. I was trying to research this topic as a friend of mine is allergic to wheat and I was curious if products that contain this ingredient would affect his skin.
Similarly, if you are allergic to dairy, would topical application of dairy ingredients in skincare products bother you?
I know people who have severe allergic reactions to peanuts can not even smell such a product, let alone put it on their skin, that is why I posed the question...