The problem with the GMO debate is hysterical people keep making unscientific objections to the general concept of gene modifications instead of specific objections to actual problems.
Monsanto makes Roundup (glyphosate)-resistant crops. As far as anybody can tell the gene modifications have no inherently harmful effect on the resulting food. But then all the crops get sprayed with glyphosate and the food is contaminated with glyphosate.
Monsanto is also very aggressive about asserting ownership of the seeds that grow from the plants that grow from their seeds. If the neighboring farm plants Monsanto crops and the seeds blow into your farm, lawyers follow. It's basically an intimidation tactic; buy seeds from Monsanto or you may end up with them anyway, and then you're going to get sued.
So farmers buy the seeds, to such an extent that it's become a biodiversity problem. Their crops are becoming a monoculture. Think systemic risk like the housing crisis, but this time it's the food supply.
In other words, there are legitimate reasons to object, even if they aren't the ones most popularly aired. So people may want to know when they're buying GMO crops and potentially contributing to these problems. Even if some people start avoiding the GMO crops for other reasons with no rational basis, that still helps with the biodiversity problem. But whenever a bill comes around to label them, guess who shows up to lobby against it.