If you're going to split hairs and say that the word God does not equate to religion, that's just silly

I'll say exactly that. The ammendment was designed to prevent the establishment of a solitary religion (ie...state church) by our government like the Anglican Church in England, where people were fined for missing church and persecuted for disagreeing with the established church.

They did not believe that all religious things should be separated from government, or they would not have opened up each of their sessions with prayer.