I've wondered if someone could be allergic to them also, so this question is very interesting to me.
Let me start by asking about your dragon's living conditions. Does it poop in the tank? If so, how often is it cleaned? what kind of substrate do you use? I've seen them in tanks with sand and we all know that any liquid can seep into that sand. Then they are essentially like a cat walking around in a used cat box. I've seen some that seem to have something caked under their claws. If the tank isn't cleaned often, we all can imagine just what it is that is caked under their claws. Then you hold them, and they scratch you. And whatever is under their claws is now in that scratch. YUK!
A lot people potty train them to go in a
bath, and then dump the
bath water. Mine is potty trained and she learned it easily. I'd call that an improvement, but I go one step further and rinse the dragon after it's pooped in the water. You can also buy a very mild soap and use that on them (just a drop!). The link below is for the soap:
http://www.beardeddragon.co/index.php?route=product/product&product_id=180
I never have any rash or allergy symptoms when I hold mine, but I think it is due to her
bathing routine and me rinsing her afterward. I remember the first dragon that I ever got having what I considered a "dirty reptile smell" the first time I held him. I didn't know about
bathing them, then, but I did read up on it after having him for about a week, and he took to potty training easily. After he died, I got my current girl as an adult, and she, too, learned very quickly. I really believe that it keeps them cleaner ( think about all of the times you've been reminded that they can carry salmonella- could this help reduce the salmonella risk?) and if you do have sensitive skin, it may be helpful for you. I'd be interested in anyone else's opinons on this topic, too!