In the Reformation, this became a major issue because the Anabaptists, of whom I'm a member, realized that the Kingdom of God meant that we would need to separate ourselves from the alliance of church and state. The trouble was that both the Roman Catholics and the Protestants had become united with the kingdoms of the world.
The Reformers claimed to be preaching the biblical faith, but they had simply changed some theology and practices here and there, often becoming less biblical than the Catholics and, for the most part, not preaching the gospel of the kingdom. We realized that if we were serious about obeying Scripture, we needed to live as citizens of the Kingdom of God rather than to tie ourselves to human government and its position of power, like the Reformers did.