I've read the Federalist papaers and even there you an see the influence of christian philosophy and thought.
Certinaly most of the Founding Fathers were Christians, and certainly there was a Christian influence in their lives and deeds. But there is nothing in the Constitution or D. of I. to show that the nation was founded on 'Judeo-Christianity.' The mere fact that citizens are given certain rights has far more to do with the English Barons who cornered King John and forced him to sign the Magna Carta, then it does to Jesus talking with his disciples (render unto Caesar).
What is the relevance of this discussion to the question of a homosexual ambassador? If the Founding Fathers intended to create a theocracy where every citizen must follow God's laws (as interpreted by ?) then Biblical references to the evil of homosexuality would be sufficient to bar this man from serving his country.
However, the Founding Fathers did not form a theocracy, instead they formed one of the first genuinely non-religious governments in history. They never referred to Jesus Christ or any of his teachings in their debates or their founding documents. The nation they created is one which values the person for what he can contribute, regardless of his religion or his parentage. That philosophy is what made America great.