Privacy is a horrible, perverted concept.. but nobody likes the smell of poo, so that's the one time you can close the door. But of course you can still open it without knocking if you have to use the shower or you also need to pee in a drain or something
We usually use the bathroom that's right off the living room. Closing the door at least partway mutes the sound of peeing and nobody needs to smell the other. It's not modesty or shyness, just courtesy. If your bathroom isn't in the middle of your living space, your results may vary, of course. :)
It is almost always open for number one. I close it for number two and wish my gf would too she "forgets" half the time it seems. I don't want to see or smell that. For me it is also some alone time where I can read like someone else said.
although you/we are all nudists at home, i think that going to the bathroom is something others don't have to see, it should be that time where you have privacy, i really don't care to watch someone male or female go to the bathroom,.