I am married and we don’t close the bathroom door. We don’t have children, and neither of us cares about the other walking past when we use it.
My husband will close the door when shaving, to prevent one of the dogs from walking in and bumping against him.
Thirded. I do pull the bathroom door most of the way closed when I take a shower but other than that the door stays open.
I live with my husband, and i don’t close the door, either. Except to shower, because we need to keep one of his drugs dry. I used to leave the door open when i showered, too.
The sight lines from the en suite bathroom go absolutely nowhere. That is, my bathroom is really two rooms, one with a linen closet and two sinks, and another with the toilet and shower. The only place you can see into the room with the toilet and shower is from the room with sinks.
Now that all the kids have moved out, i occasionally walk around the house nude. I don’t really like walking around nude, but sometimes I’ve gotten poison ivy on my pants, and want to take them off in the laundry room before going upstairs, or whatever. So i just do it, and don’t worry about it.
When i use the downstairs bathroom, i sometimes close the door to keep the cats out, and sometimes don’t.
I would like to point out that among 23 responses, I count 5 posts in which a significant factor in making the vital decision about the door involves the presence of cats, but only 1 post involving presence of dogs.
This certainly reveals important information about …something. 
I never did when I lived alone. When the kids lived here, I did. Now that it’s just my wife and me I leave it open to pee and close it to take a dump (if I’m in the upstairs bathroom; in the basement bathroom I don’t bother).
Yes. It’s a consistent habit I want to reinforce just in case I’m somewhere else.
Door closed, because if it’s open it blocks access to the toilet. Bathroom is tiny and odd-shaped.
If I was taking a leak in my married days, I’d just do it with the door open, wash my hands and be done with it. One of the first women I dated after the divorce was over at the house and I did that before we went out (we had been dating for a month or so) and she was horrified.
I have a half bath in the basement like that. I mostly close the door because otherwise there’s no place to put my legs. 
I never touch the door at all. I’m half-afraid of what I’d find behind the door, if I ever did.
When I was married (or in a serious relationship living with someone) I would close the door when doing #2 to spare the other person bodily noises and possible stinkiness.
I live alone and I do not shut the door.
FYI, this question was used as a successful junk mail campaign to get people to subscribe to Psychology Today:
”Do you close the bathroom door even when you’re the only one home?”
You just described the difference between my late wife and my ex-wife. Although the ex- remained horrified and privacy-obsessed about any/everything related to bodily functions for the whole time we cohabited and were married. She was happy to shower together. As long as none of the water that hit me bounced off and landed on her. SO weird.
Current GF and I started out real discreet, but have since settled on door closed for a dump and otherwise it’s "Door’s open; come on in! " So sensible. So useless drama-free. We both think the other is a keeper.
I live alone, but my bathroom is so tiny I have to almost close the door just to sit down.
Then my cat bops on in …
That is truly weird. I take it she didn’t swim, either.
I’m the opposite - I close it because if the cat gets in there he will cause destruction. We’re talking leaving marks on the mirror from trying to fight the other cat who lives inside it, pulling down the shower curtain, knocking my pill organizer off the counter and spilling the pills everywhere, etc.
I don’t live alone but I’m alone plenty of time, up to for weeks on end. I never close the door when I’m alone in the house. Our cat wants to hang out with me when I take a dump, but even if we didn’t have him, I’d keep the door open. But this applies 100% only for those solo times.
I have an agreement with my wife to close the door for a dump, otherwise it’s open for both of us.
I leave the door open if I’m here alone, although I also keep the litterbox in the bathroom and I wait until my cat is finished before going in there myself. She doesn’t like being “observed.”
I do close the door when I’m bathing or showering, because the cat I had before would knock things off the counter, and I simply got into the habit of doing it.
I mostly use the ensuite off my bedroom, but that might as well be an airplane lavatory, it is that small. I don’t close that door.
Everywhere else, I do. The other bathrooms in the house, I close the door. Same for hotel rooms.