Look at the EU and their policy on GMO. It is ENTIRELY fear based. They just label something as GMO which is completely useless and people are taught that GMO is bad period. Even research into GMO has almost entirely ended in Europe. It doesn't matter that their own studies show the ones they have tested are safe they continue to be against it not just in the EU but world wide. The EU is a pretty major factor in stopping the usage of golden rice.
What would you propose instead? Given that GMO is relatively new, I think it is important that GMO foods be labelled as such, so that consumers can make an informed choice. Of course, some consumers are idiots, but that's never been a strong argument against depriving the rest of us.
I'm not an expert on the topic, but it seems to me that since there is already infrastructure in place for demonstrating that the GMO product in question is safe for human consumption (which no doubt assigns it some kind of UID), simply adding the identifier to the ingredients list should be enough. It conveys to the consumer that not all GMOs are the same, while still informing them. It also makes it easy for people to google a specific strain/variant and see if any one else has reported issues.