Read Locke's 2nd Treatise. God is the foundation of natural law. Natural law is the foundation of the United States. Without God's natural law, law is arbitrary, man-made, and rights can be revoked at any time by any of man's governments.
Without natural law, rights mean absolutely nothing. Zero.
That's what "under God" means.
Someone must have forgotten to tell God about CFR.
People over the ages have been so sure that God was on their side that they committed atrocities on those who believed otherwise. (Witness the current terrorists.) Our Founders did wish to return to those times and wisely put restrictions on religion into the Constitution.
During the French Wars of Religion, a French king ordered a town wiped out and its Protestant inhabitants killed because they did not believe as he did. On another occasion at Vassy, France, armed Catholics attacked unarmed Protestants simply for worshipping in town rather than out in the fields where they had been grudgingly permitted to worship. The atrocities weren't all on the Catholic side. Once Protestants got control of a region, they outlawed Catholics.
Unfortunately, even today, well-meaning people still push their beliefs on others, like in the Pledge. Admittedly, the Pledge is not forcing someone to worship in a field, but the ghost of intolerance is there just the same.