Is the purpose of banishment to protect the rest of the tribe from the offender, or is the purpose of banishment to punish the offender?
The difference may seem academic, but I don't think the difference in attitude could manifest itself in how the banishment actually takes place. For example:
If you are part of a group of sailors that want to banish that big meanie captain and start their own little floating hippy commune, do you throw the captain overboard? Or do you throw him into a lifeboat with a radio and enough food to last until he is found?
A ship is something of a special case where the constraints require certain considerations. First of all, a ship will likely be owned by someone, who then had to hire sailors to come work on the ship. This is an excellent framework for setting up some clear rules to which those who come aboard must sign up. The answer to your scenarios lies in what those rules are. Throwing someone overboard implies violence, so that's no-go, but it's perfectly plausible that there could be a clause for a majority to buy out a minority.
To answer your answer in the more general sense: If you raped someone in my community, I might maintain that I'm not justified in causing you direct physical harm. But I do know that you're never doing any business with me. Other people in the community might feel the same, some might not, and if they shelter you, depending on the circumstances, I may or may not include those individuals in my exclusion. If I'm too broad in my banishment, eventually, I myself lose out, so there's a feedback mechanism somewhere in there. I guess that's punishment.
Of course, if you're a direct physical threat to the community, that community is justified in using proportional force in resisting that threat. That would be protection.
Sometimes it's one, sometimes it's the other. I suspect most of the times it would be a mix.
Don't get hung up on the example of the ship, obviously a ship owned by somebody else is not a good place to establish a "hippie commune" (is anywhere?).
It could however, hypothetically, be the case that the sailors felt that their lives were being endangered by the captain (who perhaps seemed intent on sailing off the edge of the world, as historically inaccurate that fear may be) and felt that he needed to be removed from command for their safety. This could be done non-violently (perhaps by simply threatening 'civil disobedience') and the captain could decide to not fight the will of the sailors and just live out the rest of the voyage in his quarters, but it is doubtful that any captain would choose that option. When this ship-turned-hippy-commune was eventually caught (the rightful owner would be furious after all), the captain certainly wouldn't want it to look like he tolerated the arrangement. The mutinous hippies, ever understanding of the captain's plight, could therefore offer the option of non-violent banishment by lifeboat.
Anyway, this non-violent banishment by lifeboat would not be done out of a desire to punish the captain. I think that banishment can either be done out of a desire to punish, or a desire to remove a threat. It doesn't necessarily need to be both, though usually it probably is. Anyway, I think we are agreeing there.
The difference may seem academic, but I don't think the difference in attitude could manifest itself in how the banishment actually takes place. For example:
If you are part of a group of sailors that want to banish that big meanie captain and start their own little floating hippy commune, do you throw the captain overboard? Or do you throw him into a lifeboat with a radio and enough food to last until he is found?
The second is not best described as 'punishment'.