You know it's possible to be against both, right?
For example: the thread here is all about how big bad megacorps have been using sophistry to hide dangerous things on their labels.
And why did this come up? Because someone wanted a giant warning that a product may contain GMOs on every product this applies to.
That's a wacko position. Why is it wacko? Well, because it does nothing to help the problem they subsequently claim to want addressed, that labels are often misleading. It actually makes the label more misleading, by highlighting a non-essential fact, giving weight to it, and pretending it's something the buyer should be concerned about, while leaving the the manufacturers to continue to do whatever they want with the ingredient list.
GMOs that do not make significant changes to a product that would leave unusual chemicals in them are not dangerous. Their presence in a food product shouldn't be highlighted as something for a consumer to be concerned about. Doing so does not give the consumer more options, it confuses them and draws attention away from real health issues like sugars and potentially harmful fats.