Sure they can, but just not in our current "captured regulator" environment.
Bear in mind that I actually introduced a GMO labeling bill in NC, but if we actually had a free market we wouldn't need it. Problem is that Monsanto owns the regulators, and sues the pants off of anybody who dares label their products "GMO-Free." Monsanto loses those suits, but not before they bankrupt the company doing it, so nobody has the guts to offer GMO free to their customers because they know that's a fast track to bankruptcy. Until we figure out how to deal with THAT, then I am willing to do GMO labeling.
Problem is that mandatory GMO labeling is a very anti-libertarian and anti-free market idea. My support for the idea is only an emergency band-aid until we can restore a real free market and not need it anymore. It will probably take another 15 years to bring about the conditions that allow GMO to be regulated by the free market, given the stranglehold of companies like Monsanto, so until that issue is solved, there are people out there who consifer GMO to be full-on poison, and they have a right to their conscience to decide that they do and do not want to eat.
So GMO labeling is just an emergency stop-gap. It kinda feels like I'm pulling a Paul Ryan "I'm voting against the free market to save the free market" in that particular arena, but I'm still of the same opinion.
The free market COULD handle the GMO question perfectly, but in our current environment it's strictly impossible. I support GMO labeling because I believe that consumers should have the ability to avoid GMO until we can restore the free market and allow the self-regulation of GMO's by allowing GMO-free products to self-label as such.
The logical solution would be to offer blanket lawsuit immunity for products that voluntarily self-label "GMO-Free" (so long as they are being truthful) but you can't do that on the state level because all Monsanto has to do is find one product that crosses the border and sue in that state to the same effect.