To me it shouldn’t matter, but it feels weird having the bathroom door open all the time. Also my shower sometimes does a midnight clunk for no obvious reason and it’s loud.
I never really thought about it until now, since I’ve never lived in a “master bedroom” with attached bathroom until now. Still on the fence, leaning towards keeping it open for convenience and airflow/dehumidification more than anything. Obviously I shut it after things get smelly.
Keep the toilet out of your line of sight when you’re in bed, that’s just bad vibes.
For airflow, open during the day and closed at night. It should have an exhaust fan, try to make sure smelly air is getting sent anywhere but your bedroom.