Man in the Funny Hat
Hero
Actions don't have alignment. My PC kills somebody. Is it an evil act? My PC kills an unarmed opponent. Is it evil? My PC kills an unarmed opponent who is begging for mercy. What if the unarmed opponent begging for his life is a CE mass murderer who has just had his weapon sundered after killing 4 other PC's in a fight to defeat him and has been in this very situation twice before - and gone on to commit more murder...You do not need to know the alignment of the PC to discuss the "alignment" of the action. You can discuss the alignment of the action without determining whether it is appropriate or not.
What your character does is almost irrelevant in the face of WHY he does it. Actions, therefore, are not aligned. The appropriateness of the action is determined by the characters existing alignment and the motivations that are driving the PC to the action.
What if the good characters believe that the barbarians actions call for immediate retribution and are simply confident that they don't need to be the ones administering that punishment trusting their comrades - and don't expect the punishment to be lethal? In that case walking away wouldn't particularly bear on their alignment. Walking away is not neutral. WHY they walk away determines if they are behaving neutrally, whether that is inconsistent with their alignment, and even if it's NOT consistent with their alignment it helps determine if the action is signficant enough to immediately change their alignment.Example: I said the two characters who walked off behaved in a neutral fashion. Consequence: If they're already neutral nothing happens, but if they're good, there's a little bit of a shift.