Were the sailors right to punish the ancient mariner? Who has the right to punish sinners in "The Rime of the Ancient Mariner"?

The ship has been drawn toward the South Pole. They are surrounded by ice. When the Albatross arrives, they treat it as a good omen. They feed the Albatross and the ice breaks, allowing them to continue on their way back north. 

The mariner kills the Albatross, seemingly for no reason. The sailors are upset because the Albatross seemed to be a good omen and they think the bird had brought them luck. After all, the ice breaks after they feed it and the wind picks up and sends the ship back to the north: 

And it would work'em woe: 

For all averr'd, I kill'd the bird

That made the breeze to blow. 

However, the fog and mist arrives and the sailors think it was right that the mariner killed the bird that brought the fog and mist. Then, the ship becomes stranded and the men are dying of thirst. Again, they put the guilt back on to the mariner, this time hanging the dead Albatross on the mariner's neck. 

It seems that they condemn the mariner for destroying their luck and/or killing an omen from God. It is not necessarily clear that they disapprove of the killing itself. In this case, they would be right to disapprove of, and perhaps even right to punish the mariner, but they do it for superstitious reasons. This calls into question the justification for their punishment of the mariner. 

The question of who has the right to punish sinners supposes that there are people in positions of righteousness who have the ethical and objective perspectives with which to make good judgments. The sailors punish the mariner for somewhat selfish reasons. They determine that their rotten luck is caused by the mariner's sin. In general, people often think of the phrase from the Bible, "Let he who is without sin cast the first stone." In other words, only those who have never sinned can punish or condemn others. This implies that no one has the right to punish another. Taking this notion with the fact that the sailors punish the mariner for selfish reasons, one could argue that their punishment is unjustified because of their reasoning. 

Had the sailors condemned the act of killing itself, their punishment would seem more just. The lesson of the poem is not the simple notion that it is bad to kill something. It has a more existential and ecological context. To be sure, it is wrong to kill for no reason. We are all part of the world, so when we damage the world, we inevitably damage ourselves. (This is the ecological, karma-themed, notion that we are all connected.) If the sailors did in fact punish the mariner for this more philosophical, ecological reason, his punishment seems more justified.

In the end, he is punished appropriately by "Life in Death." This is the punishment that actually serves a useful purpose. He must repeatedly tell his story and thus, he becomes a living lesson for others to learn. It is therefore a more logical punishment that hanging the bird on his neck. This addresses the general question about who has the right to punish others. If the punishment is appropriate in this way, the punisher would be justified. 

A punishment is more appropriate if it is done to improve the world in some way. Simple vengeance or revenge is a reactionary way to punish. This seems to be a lesson of this poem: that the punishment should serve to make things better. The mariner must become a living (in death) lesson, teaching others the hard lesson that he has learned.