Anyone who's hired as captain, or anyone who's in a position of authority for that matter, must make controversial decisions, that's why they're appointed to be captain, it's their job to make a decision whether subordinates like it or not. There will always be disent and disagreement over decisions, but it's not the role of a captain to please everybody.
The captain is not god and isn't allowed to select who lives and who dies based on her personal preferences.