Usually, it is the fragrances people build an allergy to. While the caustic stuff is formulated to rinse away, the fragrance, and other buffer material, is formulated to stick on to the material. Fabric softeners are horrible when it comes to causing allergies.
Remember, everything is made up of chemicals, natural or formulated. I have natural extracts in my lab I would never place directly on anyone’s skin. If anyone feels allergic to their washing powder, I always tell them, shift to an unscented one, any brand, and see if that helps. It usually does.
Latex allergies are very common. I am mildly allergic to it, due to years and years of using latex gloves (thinking I was protecting my skin from worse chemicals.. oh the irony). Nickel allergies are also well documented and all too common.
What we know, in the cosmetic formulations industry, is that there are well documented allergens and there are also what we call ‘sensitisers’. What sensitisers do is, when you are exposed to them, you become sensitive to things you never reacted to before, like a reaction to sunlight after applying something containing a citrus oil on your skin. It also makes you more sensitive to the next time you are exposed to them. The eugenol in clove oil is a big culprit in bath and body products for men. The fragrance that smells like rose, geraniol, is a culprit in many, many products. Some people will react, some people won’t. What I try to do, as a formulator, is take all the precautions and ensure the labels are truthful.
Tide must being using a fragrance that people have become sensitised to. That is my best guess. I was also freaked out a few times, buying products for my young son that were labelled, ‘unscented’ still contained a fragrance component in it because companies throwing that ‘unscented’ label around were still allowed to used a ‘masking fragrance’ and call it unscented.
If you are allergic to things, or suffer from skin problems, KNOW what you are putting on and around your skin. My best advice is be as informed as you can be. Know the rules and the rule breakers and read the ingredient lists.