Most GMO corn and soy actually go towards feeding animals. I can't remember the numbers but it is something around 90% of GMO corn and soy are used in animal feed, very little actually get into the human consumption. A lot of it that does, makes it into processed products (cereals, snack cakes, etc, etc).
I don't eat a lot of corn because I just don't care for it much but once in a while, I'll have polenta or corn tortillas.
You can't out-exercise poor eating habits.