You don't believe there's a God; you're an atheist. You deny there's a God because in all of their distorted everything else, they did recognize there is a God, and there's something really perverted to deny it. For this reason, again, we see this term: God gave them up to vile affections. He's going to go through a list, but it's interesting to see where he starts.
He says, "For even their women changed the natural use into that which is against nature, and likewise also the men, leaving the natural use of the woman. They burned in their lust toward one another, men with men working that which is improper and receiving in themselves the recompense of their error that was fitting."