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.
In my last apartment, the bedroom that I slept in had a sort of “open floor” layout to it, so the bathroom was kind of just there on one side, there was no door to close. It was kind of nice, I just kept an air purifier on that side of the room.