While there may well be a subtle critique going on in the New Testament of the idolatry of the state in light of the gospel, and the kingdom that brings, I think by and large the Christian faith was meant to be planted in a way that transcended any nation or government, internationally, and yet not tied down to any one nation or all of the nations put together, but very much on its own, in our American terms today: independent. The church was to be submissive to rulers and authorities, or at least those making up the church, but only insofar as that submission is faithful to the lordship of Christ. We bow the knee in the end to one Lord, and are submissive to those placed in authority insofar as they remain in their place.
In the beginning America was kind of a breakaway from the old world of church and state, but in another way, not. Yes, many people came here to have religious freedom from the state which imposed on the church much of its will in the old world, in fact we might say all of it. The roots of that is back to the Constantinian shift which began what was called the Holy Roman Empire in which only Christians could serve, everyone else essentially excluded. The Reformation in large part was responsible for this shift, though it was the Anabaptists and Baptists who pressed that. Infant baptism, except for Jews was required in the old world and was part of what it meant to be a member not only of the church, but a citizen of the state. In the complexity of that time, many came over with no axe to grind on that score, but to put their roots into the new world. Many of them were of the Church of England, Anglican, called Episcopalian here. While the new world in theory would hold to religious liberty, it was not practiced until the 1830s except for the Quaker state of Pennsylvania. This was a huge shift from the old world, yet almost the same allegiance of the church to the state remained in place. Of course with all kinds of varying understanding as to what that meant depending on the tradition, but except for the Anabaptists who were surely a relatively small minority (Mennonites, Amish, Hutterites, and the like), the state in some measure and degree could be considered Christian.
Fastforward to today. There are many who find no problem at all with pictures of the US flag draped over the cross, maybe with an image of Christ hanging on it. And even for Christians who would be uncomfortable with that, there is little or no hesitation to see the United States in its best version to be a Christian nation. Of course the US always had both believers and nonbelievers in its mix, and while scripture was pointed to as part of its original understanding of what is right and wrong, there was never any pretense on the part of the founding fathers (except for a very few) that the United States was to be a Christian nation, but quite to the contrary. They more or less invoked, or wanted the blessing of the church and of Christianity on and in their endeavor, but this was wholly another experiment entirely, steeped in the Modernist Enlightenment which was still relatively new and fresh at that time.
We have those today on the left and on the right as it’s called, who both make the case more or less of what the United States ought to look like, yes, as a Christian nation. And neither vision is the vision we find in scripture, and specifically in the New Testament in which we read of God’s grace and kingdom come in Jesus, and what form that takes through faith and baptism in the church, and instead of what place that has in the world, how the nations and the world should be seen in light of that. One might say the place the state has in the picture in which the gospel and Christ’s kingdom is the main point of it all.
And so the idea of draping a flag over a cross, or for that matter even having the US flag to be understood as basic to the identity of any church, or of course any other national flag for that matter, is idolatry at its core, or at least in danger of bowing the knee in worship to something other than the Lord Jesus. Due respect, honor and submission is one thing. But amalgamation is quite another. Churches, denominations, and individual believers have to make difficult decisions related to this, like whether or not one can be Christian and serve in the military, or in the political arena, and to what extent. But there should never be any question in all of the due submission to the state just who is lord. It is never ever the state, and never the state with the church. Christ is Lord over all, King of kings and Lord of Lords. The gospel is at the heart of our existence as Christ followers, as Christians, whether we recognize that or not. And nothing else can be a part of that.