Canned Tuna in Gluten-Free Foods, Products, Shopping & Medications Posted May 16, 2014 · Report to Admin I tried eating Starkist and Bumblebee, but I can't. It makes me sick. I decided to find out why.i looked up the ingredient I wasn't sure I could have. Soy. It turns out, soy grows in rotation with wheat crops. The farmers also use the same combine for the wheat and soy crops. Therefore, the soy is being contaminated before it ever even gets packaged. So I haven't found a single canned tuna that does not have soy in it. I'm also trying to stay safe and eat only what says "Gluten Free" on the package.