I don't know how common it is for people to become allergic to salt, though it seems like such an allergy would constitute a death sentence.
I am beginning to believe that we will have to be the death of about 50 turkeys a year, after all. I don't think I want to try barbequing a fungal turkey.
Do not think that it is a good idea to barbeque anything which has absolutely no fat. Of course you can grill veggies and suchlike, but you have to add some sort of fat or oils to them.