Well, first of all, Nero reigned from 54 to 68 AD but was only 17 years old when he came to power. Because of that, he largely followed the lead of his mother Agrippa and his tutor Seneca in the early years of his reign. He didn’t begin to take the lead until around 59 and the alleged persecutions of Nero didn’t happen until after the great fire in 64. The book of Romans, though, was penned somewhere between 51 and 58, most likely around 53 or 54. So to say that Paul was writing it in the midst of the height of Nero’s cruelty would be simply false.
Also, there’s not exactly a historical consensus on what Nero’s reputation actually was at the time. Tacitus, Suetonius, Cassius Dio, and others write negatively of him, but Epictetus, Lucan, Dio Chrsysostom, and several more wrote positively of him. Philostratus the Athenian acknowledged that he was very well liked among the common folk of Rome as well as by the provinces in the east. His style of rule was very populist and he was especially well liked among the lower class citizens of Rome, the same citizens that, presumably, would have made up the church in Rome.
Second, the tax rates of the Roman empire in the first century were about 1% and that was used exclusively on infrastructure since war was funded by acquisition of gold and silver mines through conquest. So taxes in the Roman system were much less oppressive and restrictive and didn’t contribute to the worst things that the empire was doing anyways.
Third, when Paul is talking about civil government, he almost certainly doesn’t have the emperor in mind. He’s almost certainly talking about local governors who are from the communities that they served. The system of government that the Romans instituted was one where the local authorities were left in place. There was a centralization of power in the form of the emperor, but it was also functionally decentralized in that, so long as it wasn’t causing problems for the empire, they left the provinces to govern themselves for the most part. So, again, it would have looked a lot more like a voluntary system that it would an authoritarian oppressive system.
Fourth, there’s no reason that a private, voluntary, decentralized system of civil organization couldn’t do everything that the established oppressive form of government that we see today does, while neglecting to do the horrible things that it does. Such a system would be no less in power via God’s sovereignty. Also, the gaping hole in your argument is that you seem to be suggesting that governments have no right to force us to disobey God’s law, but that they have the authority to disobey God’s law themselves, and have the right use our money to do it. I say that no man, institution, or government has the right to violate the law of God.