No, vanadium is not radioactive. The most likely ingredient that people would most commonly be allergic to is polyethylene glycol (PEG). It’s also present in some soaps, lotions, and other personal care products. I actually learned I am allergic to this a few months ago. My wife tried a new soap and I couldn’t stay in the shower with her because it literally took my breath away. Prior to that I had a coworker who’s office I avoided because she had a lotion or something that she used that did the same thing. I then bought a new fancy soap for myself and, while not as severe, it caused breathing issues and I couldn’t use it. I had heard that all the vaccines have PEG, and that it’s found in common personal care products. I then put 2 & 2 together and figured out that both the soap my wife used that took my breath away and the soap I tried had PEG. Our other soaps that don’t cause the issues do not have the ingredient. I don’t know about the former coworkers lotion or whatever but I suspect if I could see the ingredients PEG would be there. In any case, even with a legitimate allergy, good luck finding a doctor willing to file a medical exemption and, even if he/she does, the exemption goes to the state department of health and has to be signed off by someone there for it to actually be “approved”. That’s how it is here in NC anyway.