As a general philosophy I'd say no, because Muslims are commanded to follow their ameer (leader) on certain orders. It's what we call fardh 'ayn (personal obligations; i.e., not really enforced by the state), so if the ameer came and rallied the Muslims to defend the state because of an imminent threat, it becomes fardh ayn to join the battle.
In general I don't see anything in anarcho-capitalism that would prevent one from
defending his land from iminent attack. Defending a state because it is being invaded by an outside force doesn't have to mean you support the State.
It's actually a confusing set of verses, I would have imagined the third interpretation to be correct due to the persecution of Christians at this time (i.e., don't rebel, co-exist) but Paul starts by suggesting the current authority is an authority established by God and rebelling is is rebelling against God (Romans 13:1-2).
The Church authority seems more likely due to that it's been established by God, but then you've pointed out issues with that interpretation.
Do you believe Christianity to support/promote anarcho-capitalism? Even libertarianism is a stark difference to what Paul is suggesting.
I do believe Christianity supports anarcho-capitalism, although I'd be lying if I didn't admit I'm in the extreme minority on that point.
Considering, as you say, the church was being persecuted at that time, there is no possible way that the government was actually only rewarding good and punishing evil. That isn't my anarchism getting in the way of sound Biblical exegesis. That is straight Biblical fact. It is impossible that Paul is saying that the authorities that actually exist only punish moral evil and reward moral good.
Paul COULD be saying any of the following:
1. The duty of the government is to punish evil and reward good, the Christian's duty is to obey. However, these commands have nothing to do with each other (in other words, Christians must obey government, unless government commands one to sin, even if government punishes some actions that are not evil, or rewards actions to one's good.)
2. The duty of government is to punish evil and reward good. Paul's claims that governments do that is a subtle way of suggesting that governments that fail to live up to that standard (generally people who adhere to this interpretation would allow that a legitimate government could imperfectly but generally hold to it, and thus be legitimate) are actually illegitimate. This passage would still suggest that some States that levy taxes are legitimate, which means that taxes aren't always theft.
3. This passage is actually talking about the church authorities (I mentioned my questions and issues with this earlier, but its possible.)
4. As God is sovereign and ordains all things, including things that are evil (per Romans 9) God can legitimately say that he ordains the State even though the State is evil. God is saying that even though Christians are being persecuted by the State, God still intends it for their good. (I tend toward this view. It seems weird from a 21st century context, but in the context of persecution and an environment where everyone knows the State is anti-Christian, I can imagine it.
Fair point on interventionism, but don't you feel there's a difference between personal interventionism, and government interventionism. The idea of the train, is personal intervention, you're not forcing others to be put in harms way intervening for others, and I think that's the philosophic difference.
The real issue in the train case is not that you're intervening (as you say, sometimes intervention can be legitimate) but that you are killing innocent people. That's wrong. in the same way:
In my opinion if you don't like a regime across the country and think they're murdering their people and you want to join the revolution against that regime, as a personal choice, I think that's fine.
Want to join a revolution to try to kill the tyrant or his soldiers? OK. Mind you, that's a decision that you'd have to carefully consider (ie. are the alternatives any better? Killing Saddam gave us ISIS) but I'd agree that its not inherently immoral.
Bombing the innocent is a very different story. The drone strike on Pakistan that killed 30 innocents wouldn't have been justified even if it stopped a terrorist attack that would have killed 3,000, or even 3,000,000.
I suppose our difference of opinion comes from the "rigidity" in Gods laws, where I see them as general principles, where you see as it set in stone. The reason I can rationalize otherwise I think is because of intentions behind certain actions-- and this is going back to the omniscience and omnibenevolence of all mighty God.
I think there are certain things in the Bible that are general principles and others that are set in stone. Most of Proverbs is a set of general principles. Romans 13, I believe based on context, is a general principle. On the other hand, commands not to steal or murder are absolute. And some of the Bible is straight hyperbole (ie. Jesus doesn't literally want you to chop your arms off.) It depends on the passage.