And Paul was writing of a pagan government that not only had no interest in protecting Christianity, but a tendency to suppress it actively and gruesomely.
If God instituted a pagan government that turned Christians into lion excrement, then it's not a big stretch to the point where God also instituted a government based on the idea that when that government becomes destructive to liberty it is the duty of the people to alter or abolish it.
The pattern of our government is supposed to be exactly this:
We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.--That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, --That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness.
So what is it that we are supposed to submit to? The government we still have on paper, or the one that was improperly and arbitrarily built on the bodies of 700,000 dead in 1865? Did God institute that government?
I submit that if we are free to ignore what's written down, then we're free to ignore Scripture itself.
Either
1) we are to ignore the government we have on paper, and submit to the government that was instituted in 1865, which means that we're also free to ignore the written instruction of Scripture - and I therefore declare Romans 13 void
Or
2) we are not to ignore the government on paper, just as we are not free to ignore Scripture, which means we are free to actively work toward the elimination of our current anti-liberty government and replace it with one which protects our rights.
Either way, statism loses.