Guys, please help. You can see on the video my issue:
Every cold start with enabled ac I had problem with idle. On video I just forgot that temperature outside is already low, so I had to switch to lowest temperature for turning on ac and after that you can see the problem. This time engine stalled. Sometimes engine tries to fix it, but the car shakes a lot. Also, similar issue when I have to stop and switch gear to the idle and very often tachometer needle drops below normal idle, but engine immediately raises rpms. But when ac is disabled, don’t have any issues. Have new (1 year) ac compressor, freon is ok. One service said that problem could be with throttle body. They did some adaptations, got a little better but still not good. I don’t have any errors codes, nothing except this. Should I try to replace throttle body?

Video, Google Photo

Had similar issue, replaced throttle body with an ECU tune with Adrian helped the car to function where it needs to be. The final fix was the throttle body and MAP sensor but really the throttle body. also, Highly recommend an ECU tune if not already done so. EVU tune was an after thought that I should have done 5 years ago.

Hey, thanks for your answer! What do you mean ECU tune? I have some mods (newman cam PH2, 550cc bosch inj) so I did ECU tune. I heard about latest software version for ECU, but I afraid, if ask BMW to upgrade software version, my tune will be lost :(

It was just a recommendation if you did not go through a tune. Other than that, in my case, it was the throttle body. Car runs like a champ!

I am certainly no expert; but are you confident that you don't have a voltage issue or a slipping belt?
I suspect the AC would put a lot of demand on the engine and current/voltage to potentially cause diminished performance....and even perhaps stalling, rough idle/shaking (?).

Just a thought.

'New to you' as in 'rebuilt' or newly manufactured. Compressor clutch failing, or maybe internals not right?

Also, had a similar issue with AC and unstable idle right before crankshaft pulley failed (separated actually). Have you already upgraded the harmonic balancer / dampener / crank shaft pulley?

Any OBD2 codes thrown at this point?