However, the Organians did allow members on either side to get hurt or killed in the lead-up to the major confrontation.
Why wouldn't they "allow" this to happen? They show no interest in the well-being of either humans or Klingons, nor do they take a dim view on killing as such. Both sides are still allowed to kill each other, and "Organians", once the story gets going. It's just that they make so much noise playing war that the Organians get a headache.