How does our Lord interact with Earthly power structures, as opposed to individual believers?

We can certainly know one thing; the whole world lies in wickedness and in the power of the evil one, which will not be removed until Jesus returns and millenial reign is established. The evil one's power, while immerse in scope, is not absolute; he can only influence, but never directly force someone into doing something (unless in case of demonic possession) due to free will every human being had been given by the Almighty. Satan, like every ruler, requires a hierarchy of minions tasked with carrying out it's commands. Those minions form a hierarchy of their own, parallel to the human political structures and with their own ranks. We know for certain that the angel who visited Daniel had to contend with "Prince of Persia" who was a territorial spirit carrying out the tasks of the evil one within the area of the Persian empire. Both Isaiah 14 and Ezekiel 26/38 describe Satan as a ruler of Earthly political systems. The last one is of special importance of us.

Nebuchedezzar. A pagan king who razed the temple in Jerusalem is here described as "God's servant". Despite his status as ruler of Babylon and a man full of pride and sin, the Almighty for some reason chose exactly this man to witness his entire plan of human history and leave us an amazing account of his conversion in Daniel 4. Let alone Joseph, Mordechai, Ezra and Daniel (who, what most people don't realize, was third king of Babylon for a certain period of time, during Belshezzar's co-reign with his father), a pagan ruler is referred her as God's servant.

The fact that a ruler can be godly and / or be used by God, does not mean that his nation will follow. On the contrary, Joseph ruling Egypt or Daniel's governance of Persian empire hadn't turned said nations into God worshiping heavens. While a man of God occupied important (and often cheif) position, the idolatry and sin continued. This shows us that we shouldn't trust in political structures, but rather, in the allmighty. Nevertheless, a Godly ruler can always produce a lot of good and be instrumental in God's plans for Humanity (his task may be, for example, to deliver God's people from oppression as was the case with Cyrus the great). No matter of his status, each ruler is still required to follow God, was was evidenced by Herod in the book of acts.

As such, no matter the demonic structure behind political power, it is not unusual for Christians to find themselves in it. In such case, we ought to follow the footsteps of Daniel and his three friends - be in Babylon, but not of it.