A lot of the arguments I have seen have been to force producers of GMO foods to label their products as such. I take the opposite approach. If there is a sizable market of consumers who desire non-GMO foods, then there will be entrepreneurs who till produce them and label their products as non-GMO in order to capture that market.
As to the health effects of GMO overall, there is no successful business model that involves poisoning the customers. It’s just bad for repeat business, word of mouth, and potentially disastrous from a tort liability perspective.