If you don't want to have the inside doors locked then remove them.
Doesn't make sense to have that rule and to keep the locks.
If there is a lock then one has the right to privacy and to use it rule or not.
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Idk, many children still say mommy and daddy at that age. Kate's just protective, especially since Max's accident.

That part of the movie was really odd. The mom's paranoia was understandable, but you have a 9 year-old girl who was recently introduced to the family and her new father and brother are still strangers to her you should respect her need for some privacy. A girl that age is on the verge of puberty after all.
It was also odd that the dad didn't pick up on Esther's attempts to appear younger than her alleged age. She did not act like a 9 year-old. The mom realized the way she dressed was weird, but the dad didn't give it a second thought. He also kept referring to himself and his wife as "mommy" and "daddy" and encouraging her to as well. This would be odd for any 9 year-old and especially a recent adoptee.
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When I was growing up, we didn't lock the bathroom door in case of an accident, like falling in the tub. I know it's unlikely but it's just one of those things that parents often do. We also didn't look our bedroom doors when we went to sleep in case of fire or another urgent need to vacate the house. But, I also agree with your point that a self-possessed, mature girl like Esther could have been trusted to leave door locked, or to not have her mother gaurding outside. .
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I thought her locking the door intentionally was to have time to get rid of her wristband and necklace. It's obvious people don't see why would she do that.

Most parents would take note of who is in the bathroom. And many sensible people do knock before they enter. As many have said, leaving the door unlocked is a safety thing, so the parents can help if there is an accident or cry for help.
Esther just wanted the to lock the door so the family members couldn't randomly walk in and see her scars.

I know this is years late but I think locked doors are different in familes. When I lived with my parents (whether as a 10 year old or 20 year old), you did not lock the bathroom door. Shut yes, locked no particularly when you take a bath or shower. Just a safety thing.

It's a safety issue.
A family relative of mine once fell in the shower and broke a rib. She locked the door and no one was able to get into the bathroom to help her. Needless to say she couldn't move to open the door herself. The door had to be knocked down. Ever since that, I think twice about locking bathroom doors.
In house full of relatives, it isn't necessary.

I lock it if I'm crapping because my little girl will come in if I Don't lock it, she follows me everywhere. I used to lock it while I showered but I'm diabetic so now I keep it unlocked in case of emergency. Other than that, no need to lock it.

I do, lol. Guess every house is different.

My parents never wanted my sister or me to lock the bathroom door when I was taking a bath/shower. To this day, I still don't lock it.

It seemed weird to me too, but I think the mother was understood to be a bit paranoid about the safety of the kids.

It bothered me too. I can understand that rule for a very young child. But a child as old as Esther? That's just wrong. What kind of 10 year old girl would be comfortable with anyone being able to walk in on them naked or using the toilet?

We grew up knocking on doors before entering the bathroom or a bedroom.

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After watching Psycho (1960), didn't everyone start locking the bathroom door?
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Actually when I was a kid, my mom wouldn't let me lock the bathroom door. Close it, yes, but locking the door was a big no no, so it just seemed normal to me when that scene came up. In fact, in my teenage years, my mom wouldn't even let me lock my bedroom door. Some parents are just wired that way.

yep strange scene
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Some people just don't like doors locked, could be any kind of reason behind it, but its not uncommon. But the scene is meant to explain that Esther doesn't want anyone to see her naked, because she wears things around her neck and wrists to cover scars, and she also has a bandage or something wrapped around her chest to hide she has breasts. All things that get revealed later in the film so you don't end up asking how nobody noticed any of those things beforehand.

Ha, I never thought about that with Max! Makes sense, you know, the drowning aspect. But also, like the last poster said, it was to foreshadow the ending as well.

I honestly think Kate was a bit paranoid considering with what happened to Max in the past.

I grew up in the DC metro areawe did not lock the doors (you could easily see if the light was on under the door, thus in use).

Even in their own homes? I'm sure there are probably some regional or cultural differences with regard to whether people tend to do that or not. I could definitely see it if you have people over who can't be trusted to respect a closed door, for sure.