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.
At this house we keep it open- it has a nice window that i like and there’s a dog gate in the doorway. In the last house we kept it closed to keep the cats from peeing on the rug.