Comment: I believe you are confused

A republic: that form of government in which sovereignty is vested in the people and exercised by the people directly.

A democracy: that form of government in which sovereignty is vested in a whole body of free citizens and exercised by elected representatives of that body.

The United States of America as established by the Constitution is
A representative republic: that form of government in which sovereignty is vested in the people and exercised by the people either directly or by representatives who's powers are specifically designated.

A strict republic can be described as self government and can only exist in a civilized society if all members can practice law. Otherwise the people cannot exercise their sovereignty.

As far as I can tell God has no business in government. Your belief in God is between you and them. In fact, according to Jehovahs Witnesses, all governments that exist on earth today are all manifestations of satan. I am no biblical scholar but when I asked a Jehovahs Witness why he did not vote, he quoted some verse of the bible where Satan offered all the kingdoms on earth to Jesus if Jesus would call Satan Lord. To the Jehovahs Witness this was evidence that Satan owned all the governments on earth and all other governments that were conceived by man, and not by God.

Regardless, the notion of forcing your beliefs on someone else is the act of tyranny. Only a tyrant would mix government and religion.