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Well, it appears the principal problem with packaged grated cheese is
that the manufacturers often use wheat flour or cellulose (which may be
a gluten-containing item, such as wheat bran) to prevent caking and
clumping.  Also, some cheeses may contain modified food starch.
Finally, mozzarella may have vinegar in it, which is a problem for some
people.

It sounds to me like this in another one of those "if I only eat it on
occasion, and don't have a bad reaction, is it really hurting me" issues.