I actually think that ALL food should be labeled. Many organic foods where also modified using radiation or mutagenic compounds. The old style hybridization techniques are at least as dangerous and often more dangerous than genetic engineering. Just because something was done with an antique method of mixing traits between plants does NOT make it safe and free of side effects.
One of the simplest ones I like is BT toxin. BT toxin is classified as organic and safe (which it is). Organic farmers spray it on their crops and that is considered fine. However it also washes off pretty quickly. It is not very good for amphibians and some other aquatic life forms. However when that SAME thing is inserted in corn suddenly it is seen as evil. The one inserted in corn is actually better because it does not just wash off. It is part of the plant and provides much better resistance and BT does nothing to us at all at any remotely reasonable level. Sure if you ate half your body weight of it you would probably die but the same would happen with any other substance including water.
The ONLY problem I have with GMO crops is that most of them are engineered incompetently using gene gun approaches instead of restriction enzyme approaches. The current way most GMOs are done is reckless and leads to errors that are about the same kind of problems you get with hybridization techniques but still better than radiation. If monsanto and others started doing insertion with restriction enzymes or something like CRISPR-cas9 I would have no issues with what they are doing at all.
In the end the companies making GMOs are extremely lazy and that is a GREAT thing. They are not trying to make new proteins for insertion, instead they look for proteins that already exist and do what they want and they tend to only use proteins that we already normally consume from a different organism. Putting a gene that prevent ice crystallization in fish and putting it in tomatoes is a great idea. It doesn't harm you in any way but it allows tomatoes to be grown in colder climates and also for them to survive freak freezes.
If you want to label then label everything. Make a website for every food product that is run by the government that all food producers must fill out before they can sell their product. I want the full DNA sequence of all items along with all other chemicals in the food. If you genetically engineered something I want to know what method you used, what you inserted etc. If you mutated something with radiation I want to know what level of radiation was used, what type etc. Just labeling something as GMO or Organic is idiotic and definitely anti-science. It is just a convenient label for people to use that distilled down a very complex issue to some kind of bullet point. Organic is not safe or unsafe, it depends on what it is and how it was made and the exact same thing is true of GMOs. In the end we are going to use genetic engineering to make this world better and all of these stupid objections are only going to slow things down and increase accidents. There are some real objections to GMOs and also to organic farming but as long as the issues are only looked at in a very shallow way there is no real chance that we will look at the real problems with these techniques and address them.