Doctrine of non-intervention

Two questions.
1) Does anbody think that the central idea of Christ's teachings (based mostly around St Matthew's) is that one should "turn the other cheek" and affect a complete self-abnegation from the travails of the world in a way that would rule out revenge and punishment and make the legal system fraudulent
2) Is it practical... or, like so much else in the Bible, simply manner of speech?

My answer to both those questions is yes.

how can religions like Christinaity,Judaism and Islam preach 'turn the other cheek' when the unbeliever is going to burn away in hell?

fair enough

I can only partly agree. I do believe that by turning the other cheek, everyone could relieve the world around them from revenge. And if our justice system were to take the same belief, we would escape having to punish people. But this might be all it would do. You would still have to deal with the problems Decius brought up, and then try to solve the problems that would arrise from the differences between every humans' moral and ethical ideals. If we didn't, we would live within a culture that found all acts of violence and hate tolerable (well, maybe not tolerable, but unworthy of recourse). Or you could just live in a totally anarchistic society if you really wanted to.

This teaching has to be accepted within the context of the Christian viewpoint and the rest of Jesus' teachings (or a similar worldview) for it to have the value and effect that was intended. Within such a mindset you find that one must actually be trying to become an ethical/moral human being within society. Which also means everyone must have the same mindset to achieve the same results. But you probably already knew that.

In response to Angel Of Death:

Well, my answer from a Christian standpoint (although somewhat crude and unrefined) would probably be just the same as that of an authoritative figure such as a judge or an officer of the law - you made the choice and therefore you pay the consequences.

Although these worldviews teach that there are alternate places for those who choose to follow or walk away from God, they also teach that one must follow a certain path (whatever that path may be) to be considered righteous in God's eyes. For the Christian God, this would be forgiveness and repentence (turning from the path that would lead one to hell and beginning an abundant life under God's sovereignty). You should also note that all people are separated from God at birth and considered unrighteous. So in the thick of it all, it comes down to the choice of the individual: do you understand God's love and wish to be as though one of his children? or do you wish to be free of righteous living as according to God and follow your own way?

This brings you to the consequence of hell. How do you know if hell is fire and brimstone anyway? The Bible (in the Christian context) also describes hell as separation from God, and as destruction (annihilationism). The only thing that one needs to know is that it is better for a person not to go there.

It is also noteworthy to mention that there aren't any definite answers as to the destination of a soul who has never heard of God. But in a Christian worldview, it is up to us to make sure everyone has heard.