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Hi, I too have wondered about this.

I fit in much them same category as yourself although I am not Irish. :)

I am intolerant of milk and all grains with gluten. I have not been dx
with cd or sought it as makes no difference to my outcome as I am
miserable on gluten.  I doubt that I would be positive on testing as I
do not have the severe sx that generally are assigned to cd. I was
treated, without success, for my "wheat " allergies which like you
included reaction to rye etc. Only after I noticed that was only gluten
grains and eliminated all of them, did I get better. Non of the
physicians considered that and did not think I could have cd. To get to
your question, I think that there may be kind of "soft" or sub clinical
cd that presents with less intense sx.The whole thing is complicated
because of the damage to the gut from the reaction to gluten, one can
develop what is known as "leaky gut" syndrome which translates into the
gut permitting leakage of large protein molecules into the blood stream
which are perceives by the body as foreign and one develops an "allergy"
to that food.

June