Are you buying the paper cores to use in a film/bag making process of your own? Or is your bag/film supplier telling you they use paper cores that contain wheat starch for film you purchase? Have you gotten a paper core tested for presence of wheat allergen or gluten?
If you're a film manufacturer, I'd easily look at other paper roll providers who either don't use wheat starch or are willing to certify it poses no allergen risk. There are too many other real hazards in our day to day to deal with a manufacturer who won't meet modern demands of purity when it comes to allergen controls.
And for me, this highlights a hugely under looked risk in packaging, where food allergen containing components are utilized in place of non-food grade toxic components. In my first job we had pink colored poly drum liners for a specific customer, who gave us documentation that the pink dye in the poly liner was derived from shellfish husks. Weirdly enough a couple of our auditors actually asked if knew what the dye was derived from, but luckily we had documentation in hand that the dye lacked any shellfish proteins and was sandwiched between two clear inert layers of plastic in the manufacturing process.