I've always felt that this was short0-sighted (a typo, but one I will leave in) on US producers' part. A great many countries embargo US crops and foodstuffs not just because they were composed of unlabeled GMOs, but also because we like using food dyes and additives that are unlicensed outside the US/Canada. For these reasons, the American notion that we "feed the world" is risible.
For the small price of not using these obnoxious additives -- and the slightly greater price of changing suppliers and distributors to avoid now-unlabeled GMO products -- US foodstuffs could find greater acceptance and marketshare abroad. Any country that then refused American food products can rightfully be accused of protectionism.
Stop trying to convince foreigners that these adducts are harmless, and just sell them what they want.
Cite that American food producers are suffering without these markets?