<<Disclaimer: Verify this information before applying it to your situation.>>

I e-mailed Sargento asking for their GF cheese.  Here is their response.
They answered me as soon as the day after.

We are pleased to tell you that most Sargento natural cheeses should be
acceptable to a gluten-free diet.

There are a few exceptions.  Sargento Shredded Imitation Mozzarella
Cheese contains a modified food starch which may contain gluten.  We
would also not recommend that anyone on a gluten-free diet eat our
Shredded Taco Cheese, our Shredded Nacho & Taco Cheese, or our 6 Cheese
Zesty Mexican Recipe Blend.  There is wheat flour in the spice mixture
in these products.  For obvious reasons, we would also not recommend
our MooTown Snacks Cheeze & Sticks, Cheese & Pretzels, Cheeze &
Crackers, or Cookies & Creme.

You will notice that we use microcrystalline cellulose as an anti-caking
agent on most of our shredded cheeses.  When added to shredded cheese,
cellulose prevents the shreds from sticking together.  Microcrystalline
cellulose is a white, odorless, tasteless, totally natural powder made
from cellulose, a naturally occurring component of most plants.  It is
not derived from wheat, oats, barley, or rye.

We hope this information is helpful.  If you have questions about how
our products may affect your medical condition, we suggest you discuss
this information with your physician.