"Let every person be subject to the governing authorities; for there is no authority except from God, and those authorities that exist have been instituted by God. Therefore whoever resists authority resists what God has appointed, and those who resist will incur judgment."
What God has willed is "governing authorities", this does not say that God hand-picks individuals, or gives tacit approval to whoever happens to be in charge. It means that civil power exists for a good purpose and is this way by divine design. The "authorities" here probably shouldn't be confused with persons with authority, but rather refers to the act of holding power/authority itself.
God did not personally make Nero the Roman emperor; but the act of rule which Rome has--to maintain the rule of law where it has jurisdiction--this ultimately does come from God.
"For rulers are not a terror to good conduct, but to bad. Do you wish to have no fear of the authority? Then do what is good, and you will receive its approval; for it is God’s servant for your good. But if you do what is wrong, you should be afraid, for the authority does not bear the sword in vain! It is the servant of God to execute wrath on the wrongdoer. Therefore one must be subject, not only because of wrath but also because of conscience. For the same reason you also pay taxes, for the authorities are God’s servants, busy with this very thing. Pay to all what is due them—taxes to whom taxes are due, revenue to whom revenue is due, respect to whom respect is due, honor to whom honor is due."
Civil authority wields a sword (literally and figuratively) to address violations of the rule of law, and Christians are not called to be law-breakers. Instead Christians are called to be humble servants and act in accordance with the rules of law where we live. This civil power, which exists from God, exists to curb civil evil. If I run a red light, I'll receive a ticket and a fine--as a Christian it would be wrong for me to violate such laws and if I did it would be proper for me to, for example, receive this fine and in turn pay it and acknowledge where I have erred.
At no point does any of this mean that God personally makes someone king, emperor, president, mayor, or school class treasurer; that such persons are owed any kind of absolute allegiance, or that any temporal system of power is to be obeyed unquestioningly. As the Christian confesses one God, the Father who is over all, and one Lord Jesus Christ.
"Owe no one anything, except to love one another; for the one who loves another has fulfilled the law. The commandments, 'You shall not commit adultery; You shall not murder; You shall not steal; You shall not covet'; and any other commandment, are summed up in this word, 'Love your neighbor as yourself.' Love does no wrong to a neighbor; therefore, love is the fulfilling of the law.
Besides this, you know what time it is, how it is now the moment for you to wake from sleep. For salvation is nearer to us now than when we became believers; the night is far gone, the day is near. Let us then lay aside the works of darkness and put on the armor of light; let us live honorably as in the day, not in reveling and drunkenness, not in debauchery and licentiousness, not in quarreling and jealousy. Instead, put on the Lord Jesus Christ, and make no provision for the flesh, to gratify its desires."
We acknowledge that all authority ultimately belongs to God, and temporal authority exists only from God, for but a season, for the civil good of human society. This temporal authority has no permanence, is not owed any kind of ultimate allegiance, and it serves the singular purpose to maintain the peace and for civil justice in this present age.
-CryptoLutheran