There is no logical way to successfully separate 'religion' from 'law and history' in the context of the Founders' Original Intent. That's why there is a First Amendment - to prevent a state-imposed theocracy. It does not negate the fact that their Original Intent for The Republic was driven in large part by their belief and acknowledgement of a Divine Authority over Man. It is part and parcel of our framework and our culture. To attempt to clinically dissect it, or view it with the politically correct implication that the concept of a guiding Higher Power might be some esoteric quirk in the minds of the men who drafted the purpose for this nation's existence, merely diminishes the value of everything we have spilled our blood to preserve.
The 1A originally was a restraint on the feds, not the states. Several of the states had estabished religions as late as the 1830's.
Picking a version of the Word of God and posting it in courthouses certainly sounds like state-imposed theocracy to me.