If you are in any doubt as to the meaning of these verses due to the archaic language, here they are again in the NIV translation:

Let everyone be subject to the governing authorities, for there is no authority except that which God has established. The authorities that exist have been established by God. Consequently, whoever rebels against the authority is rebelling against what God has instituted, and those who do so will bring judgment on themselves. For rulers hold no terror for those who do right, but for those who do wrong. Do you want to be free from fear of the one in authority? Then do what is right and you will be commended.

These words have been used over the centuries by those in power to control the masses, to 'crush dissent, stifle protest and discourage civil disobedience.'¹ But it must be remembered that Paul wrote these words whilst in prison—in prison for insurrection. Paul had broken Roman law by preaching the gospel of Christ and undermining the status quo, yet here he is apparently telling everyone else to do what they're told. Isn't that hypocritical? To understand this directive in its full context we need to go back a few verses to 12:14, remembering that the chapter breaks were arbitrarily added a few centuries after the books of the Bible were written. It is reading Romans 13 without context that has caused so many of the problems we associate with this directive.²

In Romans 12 we read: Bless them which persecute you: bless, and curse not. Rejoice with them that do rejoice, and weep with them that weep³ and goes on to advise, Therefore if thine enemy hunger, feed him; if he thirst, give him drink...Be not overcome of evil, but overcome evil with good.⁴

In other words, love your neighbour, as the Torah tells us, and also love your enemy, as Jesus tells us.⁵ Withhold violent response. Vengeance is the Lord's. Instead of violent reaction consider instead peaceful resistance. Break the law if you must, but do it wisely and calmly—and be willing to face the consequences. That's the nub of this. The laws are there for a reason, and most laws are good laws. When they are bad laws, or enacted unfairly, protest them, but with caution, and if arrested go—like him, and indeed like Jesus—placidly to whatever justice the society decides is appropriate for your transgression. Paul is less afraid of Christians being killed than of Christians becoming killers—and thus sinners in the eyes of God. Violent resistance will lead inevitably to the latter.

Jesus came to teach us that there was a third way to confront oppression: not violence, and also not passivity and compliance. The way that Jesus taught is the way that Paul continued to teach: resist oppression with love.⁶

¹ No, Romans 13 is not about obeying the governing authorities, by Craig Greenfield, 2018
² Once again I refer the reader to The First Paul: Reclaiming the Radical Visionary Behind the Church's Conservative Icon by M.J. Borg and J.D, Crossan, pp 117-120
³ Romans 12:14-15
⁴ Romans 12:20-21
⁵ Matthew 5:44
⁶ This was also the approach that Martin Luther King Jr favoured: love your enemy until they learn to love themselves, for when a person loves they are incapable of hate.