What should I do?
I removed my step daughter’s door for the same reason, at the same age. She had a bad habit of slamming her door, or should I say, MY door, when she was angry.
We gave her fair warning: slam the door one more time and I will remove it. Well, it was about 30 minutes after giving her the warning when she slammed the door again. I proceeded to get a hammer and screwdriver and removed the hinge bolts and removed the door. I told her that she could have the door back when I believed that she will use it appropriately.
Removing the door wasn’t done lightly. She was told what would happen if she slammed the door again. Therefore, she had full knowledge over the possible outcomes: close the door properly and keep it; or slam the door and lose it. These were her options and she had full disclosure of the consequences of her actions, but decided to slam the door nevertheless.
The key here is to ensure that your children are aware of the consequences prior to acting on the unwanted behaviour. If they continue with the behaviour after having this knowledge, it is on them and not the parent. Failure of the parent to not follow through with the consequence will guarantee that the child will view this, and other consequences, as empty threats. At this point you lose credibility.
Did my actions correct the unwanted behaviour? Absolutely! I haven’t heard a door slam since. Also, she learned that when we advise her of potential consequences to her actions , we follow through with it.
To answer the question directly, stop slamming the door and you will maintain your privacy!
Edit: my stepdaughter’s privacy was never an issue, as her bedroom was the only one in the basement. She basically had her own self- contained living quarters in the basement, with the exception of a kitchen.

Let me first say that I don’t agree with taking away people’s doors. I think people, teens included, need their privacy.
However, if you knew that they didn’t want you slamming the door, they had told you not to, then this one’s on you. The only thing you can do is wait until you have earned their trust again and they feel they can give you the door back, then never slam it again.
P.S. I get asked a lot “Why do you disable comments?” It’s not at all the reason people think. I can take people respectfully disagreeing with my answers, or adding to them. What I can’t stand is when people write THEIR OWN ANSWER to the OP in the Comments section. They are either 1. too lazy to click on the original question, 2. hoping to get lots of view and upvotes by piggybacking off my answer, or 3. just too stupid to understand how Quora works. And that is why I disable comments.