The problem here is your use of the word "sin."
I don't think Paul had any intention of implying that Emperor Nero respected the concept of "sin" as Paul himself did.
I did not use the word “sin”, I used the word “sinful.” *pulls out my English major card and puts it on the table* “sinful” is an adjective. There is a difference.
The truth I was alluding to is fairly simple: without sinful people, there would be no need for human government. Frankly, is it not the sin nature of mankind that inspires us to rule over, dominate, and deprive one another? Ignorance or rejection of a concept does not mean that it does not govern (pun alert!) or define your reality.
Romans 3:23 is still true: “All have sinned, and come short of the glory of God.” and I do believe that all means all. That means that atheists have sinned (even though they don’t acknowledge it), Nero has sinned, and everyone else who will never acknowledge sin as a valid concept has sinned. Therefore, sinful is a valid adjective to describe everyone, regardless of their belief system. Romans 13 must be interpreted in context of Romans 3; Paul is not contradicting himself within the same letter to the same people who would be reading the whole thing.
This really gets into my belief that truth is truth, regardless of what I believe to be true. If a rock is 5 meters away from me, I can believe that it’s 6 meters away all I want - get the tape measure out, it’s still 5 meters. I can believe I’m not female all I want, that doesn’t change the fact that I am female, complete with two X chromosomes and female reproductive organs. Likewise, I am a sinful human being, and I can not believe that all I want, but that doesn’t change the fact that I am a sinful human being.
You actually don’t need to believe in Christianity to believe what I just told you, because science claims that not perceiving or believing reality correctly is a mental disorder. We call it trauma, bipolar, depression, ocd, just to name a few of the perception disorders science has named. Obviously the sin nature of mankind wants to become God and control everything, so it’s going to shrink God down and perceive reality incorrectly. The problem with blaming mental disorders on the people who have them John MacArthur style is that our fallen bodies can be damaged by sin that is not our own. We can be lied to. We can believe lies. We can be hurt by others. It’s not just that we have a sin nature that wants to believe distortions, we live in fallen bodies that are so damaged and weakened by the sin of ourselves and others that they react in disordered fashions and produce inaccurate perceptions without our full conscious intention. Never mind the fact that our perception is limited by our fallen senses and is thus incomplete anyway, which might explain my lack of ability to estimate the distance between me and a rock with any sort of accuracy.
But despite all that, the rock is still 5 meters away, I am still female, I am still a sinful human being, and Jesus Christ is still Lord. The truth has not changed, and my mind, apart from my body’s ability to manipulate immediate reality, cannot change the truth. The only power it has is to know the truth and accept it, and then to act on it. Hence our ceaseless wrangling in educational systems to subdue our fallen nervous systems and force them to perceive truth.
Anyway, I don’t think Paul is making a personal comment on Nero here, simply a philosophical statement about government and its role. The role of government “is to punish those who do wrong and reward those who do right” which then means that government is a restraining device for sinful people. Sinful people are capable of doing wrong that can be punished, and need incentive to do right that can be rewarded. If we were in glorified bodies in the New Jerusalem, God would be our King, Lord, and authority to which we would submit perfectly, but we relate to Christ as his Bride and to the Father as his Sons. The level of intimacy there really precludes that being like human government as we understand it, more like a large family. People in glorified bodies are incapable of doing wrong, and if we do right, that is because of Christ’s sacrifice and so why are we being rewarded?
This philosophy does not preclude the idea of bad government, such as Nero. The idea is for a Christian to roll along with human government as a natural way that the sinful people restrain themselves, rather than the actions of specific evil rulers. We submit to the office and authority, not the person, in these scenarios, and then file our grievances and appeals later, unless the government has set itself up in opposition to the Gospel, in which they have placed themselves on the opposite side of Ephesians 6 and shall be subject to spiritual warfare. The rulers and principalities we war against when they are instruments of Satan. That would apply to Nero, obviously. Paul is not contradicting another letter he wrote to another church with Romans 13.
Keep in mind though, there is a difference. Rome was the seat of secular power, and the Ephesian church was fighting the temple of Artemis and submission to an idol. If the Roman church failed to submit to the Roman government, they were in Rome and thus would not last very long, but in Ephesus the spiritual battle was pitched against the lies and customs of Artemis that were against God’s Word. The authority had set up a false god to be worshipped, similar to the story of Nebuchadnezzar in the Book of Daniel, which Paul knew very well.
This is how we arrive at “submit to the government unless they force us to silence the Gospel and act against the Scriptures” principle for Christians today. No Christian shall be obliged to worship a false god because of an authority, or to cease proclaiming the Gospel, and so we continue.