How can I tell which beauty products or cosmetics are safe to use on a wheat or gluten free diet?
Generally beauty product/cosmetic manufacturers tend to use the word "triticale" instead of "wheat" in their ingredients lists.
Before purchasing a beauty/cosmetic product you should always read the ingredients listed on the packaging. Sometimes it's so small it's impossible, so I'd suggest you carry a tiny magnifying glass with you on shopping trips, or get an app. It may look a little weird, but it's preferable to buying something that may iritate your skin or make you sick if you suffer from a wheat allergy/intolerance or celiac disease.
Some beauty products do contain allergy information e.g. contains wheat, however they're in the minority.
There are also many other alternative names for wheat, but these are generally more likely to be found in food products.
When I go to the hair salon I tend to not make a big deal about the stylist using products that have wheat in them as it's a one-off and also uncontrollable situation. I just don't touch my hair, eyes, mouth etc. until I've had a chance to wash the products out completely. This will not, however, be a suitable option for people whose skin reacts to wheat. I also never allow any massage oils or body lotions to be applied that contain wheat.