The site they link to warns of the dangers but never says what they are. Then, if you dial in to a PDF buried on the site it finally stated this:

Peer-reviewed studies have found harmful effects on the health of laboratory and livestock animals fed GMOs. Effects include toxic and allergenic effects and altered nutritional value. u Most animal feeding studies on GMOs have only been short-term or medium-term in length. What is needed are long-term and multi-generational studies on GMOs to see if the worrying changes commonly reported in short- and medium-term studies develop into serious disease. Such studies are not required by government regulators. u Industry and regulators dismiss findings of harm in animal feeding trials on GMOs by claiming they are “not biologically significant” or “not biologically relevant” – scientifically meaningless terms that have not been properly defined. u No GM nutritionally enhanced (biofortified) foods are available on the market. In contrast, conventional plant breeding has successfully and safely produced many biofortified foods. u The most-hyped GM nutritionally enhanced food, Golden Rice, aimed at combating vitamin A deficiency, has wasted millions in development funds – yet has not been proven safe to eat and is still not ready for the market. Meanwhile, proven and inexpensive solutions to vitamin A deficiency are available and only need proper funding to be more widely applied. u Conventional plant breeding has successfully and safely produced many biofortified foods.

-allergy and altered nutritional value? That's all you've got? I can see wanting more research in to the effects, but in the absence of that research, making it appear to be evil just seems wrong. Brilliant marketing by the non GMO people. My guess is that there are a lot of hungry people in this world that could care less about GMO.