My feeling is that I support neither. But for me it's sort of like worrying about the fact that the handle is loose on a door that's been blown off its hinges. I don't support much about the U.S. government anyway.
My reason for not supporting "one nation under God" or "in God we trust" are for one I'm not Christian, so why would I support such a thing. Also, I think that putting the name of God on money is kind of cheap and tacky, and insults Christians and their God. And though I'm not a Christian, the idea of "God" in a non Judeo-Christian sense still has significance for me. Hell, God in a Judeo-Christian context has significance to me as well. I grew up surrounded by Christians, and if not for the Christians, how would I ever have developed my cynical nature? So, I'd like not to have the God who I have no faith in, but owe my lack of faith to, cheapened.
The "one nation under God" phrase I'm opposed to for similar reasons, but my solution to that is just to not say it whenever I'm reciting the pledge of allegiance.
"Far from being rivals or enemies, religion and law are twin sisters, friends, and mutual assistants. Indeed, these two sciences run into each other. The divine law, as discovered by reason and the moral sense, forms an essential part of both."
--James Wilson, signer of the Declaration of Independence and future Associate Justice of the Supreme Court, 1791
Such attitudes are found throughout much of the writings of the founding fathers.