AirPods beeping and failing connection to MacBook

My AirPods work well with iPhone, but when trying to connect to MacBook:

1. I see that they are connected.
2. Left or right of them starts beeping constantly (with sound which is played when they are put in the ear, but beeping very quickly).
3. After a couple seconds of that beeping they go disconnected, then connected again automatically, and all that stuff repeats (go to Step 1).
4. So, I'm unable to connect them to my Mac.

They don't connect to any MacBook (I tried couple of them, Mac OS Catalina, newest version).

Of course:

* Unpair/Pair doesn't help.

* Resetting the AirPods doesn't help.