I solved this by letting the cat open the door from both sides.
From one side, the cat can just push open the door. The closing force on the door comes from a small weight hanging on a string, which goes from the top corner of the door to an eye screw on the wall and down to the weight. The weight is adjusted to be just barely enough to pull the door closed, so the door is easy for the cat to push open. The cat walks through and then the door closes very gently and quietly.
From the other side, the cat can pull open the door. I stuck a little hook-handle on the bottom corner of the door, and the cat learned to paw the handle and pull the door open. Because the door closes so slowly and gently, it's easy for the cat to get through.
This lets the cat can come and curl up with me whenever he wants. It's quieter than a flappy cat door; he can come and go without bothering me or waking me up.
I have the same cat friendly door closer! Very useful for a good night’s sleep. But now my cat is so old he mostly stays curled up on the bed poor fellow.
Heads up that a) those commercial/industrial door closer thingies aren't that expensive if the door isn't too heavy, but better than that b) they have spring door hinges, so you can install those and the door will self-close. Not sure its cat friendliness but it works for keeping the door closed.
From one side, the cat can just push open the door. The closing force on the door comes from a small weight hanging on a string, which goes from the top corner of the door to an eye screw on the wall and down to the weight. The weight is adjusted to be just barely enough to pull the door closed, so the door is easy for the cat to push open. The cat walks through and then the door closes very gently and quietly.
From the other side, the cat can pull open the door. I stuck a little hook-handle on the bottom corner of the door, and the cat learned to paw the handle and pull the door open. Because the door closes so slowly and gently, it's easy for the cat to get through.
This lets the cat can come and curl up with me whenever he wants. It's quieter than a flappy cat door; he can come and go without bothering me or waking me up.