Does humanism's rejection of God necesitate relativism?

I had the following discussion on Programmers.SE: @Peter Turner, Which is a good example of how religion warps morality, leading people to imagine their concerns are moral when they are profoundly immoral. – TRiG @TRiG, Which is a good example of making an appeal to absolute truth where you would normally appeal to relativism. The problem is, you don't listen to our arguments and you assume they're all appeals to something you don't believe in. Whereas, Catholics almost always argue for morality in a non-dogmatic rational way. – Peter Turner @Peter, I don't think I've ever appealed to "relativism". I'm familiar with Catholic "Natural Law" argument, and I know it's nonsense. Humanism is not relativism. But perhaps discussion on these lines would be better on the philosophy site. – TRiG This discussion made me question whether I was really correct in assuming that humanism's rejection of God necessitates a belief in moral relativism. I found the following definition of humanism, which seems to back up my thinking: Humanism's exclusion of God necessitates moral relativism. Humanist John Dewey (1859-1952), co-author and signer of the Humanist Manifesto 1 (1933), declared, "There is no God and there is no soul. Hence, there are no needs for the props of traditional religion. With dogma and creed excluded, then immutable truth is also dead and buried. There is no room for fixed, natural law or moral absolutes." Humanists believe one should do, as one feels is right. Is there any evidence to the contrary?