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.
Normally closed. Simply because I like doors closed in general.
A second reason is sometimes that I like to have it really dark in the night, but sometimes light comes in through the bathroom window.