What does it take to handle interactions with emotionally immature people?

There's a primary conversion that needs to take place: from reactivity to observation.

Emotions may still arise. Your physiology may be spurred into fight or flight from someone else's frustration, rage, outburst. There's no shame in being a social and empathic animal.

The trickiest part is transmuting those emotions into positive action with calm and grace.

Observe the emotions from without and from within. Let them pass and go through their course. Then take action.