I will be adding to this post.
To me, it is just as important when debunking quack claims, to offer people reputable sources, for reputable information.
"Should Your Children Avoid Gluten?", 2013
"7 Myths and Facts about Celiac Disease", 2014
" Myth 5: Kids with celiac disease have to use gluten free soap, shampoo and lotion.
Fact: Gluten cannot be absorbed through the skin, but parents need to be aware of hygiene products that are easily ingestible, especially when bathing younger children."
"Cosmetic Labelling Regulations", 2013
"To date, we have been unable to find any toothpaste that contains gluten."
"Action Alert: Notifying the FDA about Misbranded Gluten-Free Products" | Gluten Free Watchdog, 2014 https://www.glutenfreewatchdog.org/blog/Action-Alert-Notifying-the-FDA-about-Misbranded-Gluten-Free-Products/37
"Foods Labeled Gluten-Free Must Now be in Compliance with the FDA Gluten-Free Labeling Rule" | Gluten Free Watchdog, 2014
"Gluten and Food Labeling: FDA's Regulation of 'Gluten-Free' Claims" updated, 2015
"overblown claims for “going gluten-free,” and ridiculous products such as gluten-free skin care products"
Therein lies the "rub" (quandary) to quote Shakespeare. If a cosmetics manufacturer is claiming gluten-free for certain products, can that claim be trusted?
If said cosmetics manufacturer, or anyone promoting them also makes outrageous (health fraud), or drug claims with no proven evidence for those claims, most probably not. They don't have credibility. If you have celiac disease, or young children who do, it is best not to take a risk with such a company for any products needed. Consult with your medically qualified specialist for recommendations.