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Take sides
Neutral Implication
Using 'take sides' often implies the situation is not one's personal conflict, but choosing to support one side over the other. 
Emotional Intensity
'Take sides' can suggest emotional involvement in a dispute, indicating support is not merely logical, but also emotional. 
Conflict Avoidance
'Refuse to take sides' shows a deliberate avoidance of conflict, used to maintain neutrality or peace. 