Can a person be considered healthy and still have allergies of some sort?
A person can still have good general health and still experience allergies. Of course some of them are super dangerous or right down deadly, but as long as you don’t get in contact with the allergens, or you respond quickly (have medication near you), allergies in general don’t indicate how healthy you are overall.
Some people would say the are allergic to gluten, but that’s actually an autoimmune response and not an allergy. This is called Coeliac Disease.