Roy Moore's spokesman was utterly stumped when he learned that people can be sworn into office with a text other than the Bible. His interview betrayed an ignorance of the U.S. Constitution, particularly the Establishment clause that bars the U.S. from having an 'established religion'. At the time of the signing of the U.S. Constitution, the Christian monarchies of Europe had established religions. Many of these monarchies proclaimed their King or Queen had been chosen by God to rule .
For instance, the United Kingdom had (and still has) a state church called Anglicanism (the U.S. variant is called Episcopalianism). Other countries, like Saudi Arabia, have an official religion, meaning that everyone in the country must follow the Saudi interpretation of Islam or face punishment.
Beginning in the 1970's, the American Christian Right began claiming a revisionist history of the American founding, claiming that the founders were essentially theocrats. In reality, the Founders, who knew the history of their native Europe, intentionally chose not to establish an official faith.
[In] the text of the Constitution, religion was deliberately kept at arm's length from the state. In radical departures from the era's norms, there would be no religious tests for federal officeholders, no establishment of any national religion and no congressional interference with individual citizens' free exercise of their own faith. This was no accident. Despite their respect for religion and their belief in the divine origins of human rights, many of the Founding Fathers worried that religion would corrupt the state and, conversely, that the state would corrupt religion.
In the century just prior to the founding of the U.S., Europe had convulsed during a series of religious wars, most notably the Thirty-Years-War, fought almost entirely in what is now called Germany. Historians believed that the war was so catastrophic to life and property that it set Germany back at least 200-years.
The 30-Years-War was second only to World War II in its catastrophic destruction of Germany. Fields were devastated, whole villages and farmsteads systematically burned, churches and schools destroyed, animals slaughtered, women kidnapped and raped, men murdered. Epidemics and hunger killed tens of thousands. The 80,000 population of Augsburg was reduced to 18,000; that of Wuerttemberg from 400,000 to 48,000. Berlin only had 300 residents left at the end of the war. It is estimated that the 18 million population of Germany was reduced by two thirds to 6 million. The economic, political and intellectual consequences of this war set Germany back 200 years.
There was not an independent and sovereign Germany until 1871.
So, the idea that the founding fathers would have been theocrats in the mold of unelected monarchs of their day seems quite far-fetched, particularly because they wanted to prevent the religious wars of Europe from happening in the United States.