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.
My master bathroom (attached only to my bedroom) door generally stays open partly because the toilet has its own micro-room with its own door that can stay shut, partly because the dog likes lying on the cool tile, and partly because the HVAC system is more efficient that way.
I also have a bathroom between two rooms. My office and kids’ room share one. The office door stays shut all the time. The kids’ room generally stays open for a little additional light, to reduce accidents because they were sleepily fumbling with the door and because kids are inherently kinda lazy about things like closing doors.