Try to see the actual values in the engine and AC control units. This system does not work as in the old days. The AC request the compressor load from the DDE (engine computer) and DDE activates the compressor. It is not ON/OFF type, the load can vary from 5 to 95% or so. Not 100% sure for your car, but the newer ones are not a clutch type, but have a internal vane inside that moves back and forth and changes the volume the compressor is pumping. There is a lot of info around, you have to search.
Below is a link to a very interesting forum. On the 4th page there is a manual for the E70 AC.

BMW x5 e70 - BMW forum. Diagnostics, coding, programming, repair BMW vehicles.