Hmm... I can sort of see your point, but would you mind telling me why it is absurd? I mean are allowed to know what they're eating right?
Give Headcrab Zombie and SeventhSandwich's posts above a read.
The issue with forcing a GMO label on GMO foods is that it negatively targets GMO foods. Those entirely uneducated in GMOs (such as those 80% in the study linked earlier who didn't know the difference between GMO and DNA) may entirely boycott lots of products simply because they contain GMO.
And the issue is that GMO is a completely blanket statement.
We're doing all sorts of things via genetically modifying our food.
That includes such things as allowing crops to produce their own insecticides or herbicides (which some might be wary of, as traditional pesticides can have adverse effects on local habitats or be unsafe to consume).
It can also be creating a crop that produces extra vitamins. Vitamins that are useful in keeping people healthy, such as removing deficiencies in populations around the world (these would really be no more harmful than taking vitamin supplements).
And then you can hopefully use them to provide disease resistance or immunity to those who consume them.
And then you get the more novelty situations, as Harm has mentioned, where unusual traits from certain animals (such as bioluminescence from things like squid and octopus) are given to other creatures, like rabbits (so that they glow in the dark). These as far as I know, don't end up in the food chain (because they serve no benefit as a food item) and are just for research, so some people disagree with them because they see it as cruel on the animals involved, or it's needlessly "playing God".
So imagine that you've got a situation where all GMO foods are labelled GMO.
And you have a population of around 80% who don't really understand GMOs, but they've heard of them.
And perhaps they've seen the glowing bunnies, or heard of the crops that produce their own pesticides, and they don't like those (as it's their right to feel about such matters).
They obviously don't want to buy or support those products, so any time they're in the shop and they see a GMO label they say "No! I'm not buying you!".
But those labelled items aren't just glo-bunnies or pesticide GMOs, they're good vitamin-rich or disease resistant, or immunologically beneficial crops/foods. Those companies start losing money because everyone stop buying their products, because they've confused them with other products, and now these companies can't afford to produce their GMO crops, so the developers/researchers of those GMOs also can't afford to continue researching them.
The way around this ties into the labelling system again, whereby farms that use GMO crops detail what exactly it is that these GMOs are for (whether being pesticidal, or producing vitamins).
And then your products need only state their sources.
You go online, perhaps to a database of this big government/3rd party organisation who is keep a record of all these farms and their practices, you search for the farm mentioned, and there you go, you can research what you're buying and choose to spend accordingly.