I don't shut my bathroom door, but then, I live alone.
When I'm in a house with other people, I not only shut the door, I consider the door to be absolutely, 100% soundproof if I am using any plumbing fixture other than the sink. That is, I am unable to hear requests to open the door, or attempts to converse with me. Nope, can't hear you, dude. Using the bathroom is not a social occasion.
Well, it might be, but then, the other person would be on the same side of the door as I am.