I had the exact same problem,
I was running stock measure 225/40-18 and 255/35-18 but different brands,
used Michelin's front and new Hankook S1's rear.
The dealer always blamed them for not being RFT's,
showed me that by putting on all around 225-17 BMW RFT winter tyres the problem went away.
Of course they wanted to sell new BMW tyres.
They never said that the only reason was the different running diameters.
I then asked for a piece of electrical wire, about 2,10m long and measured the circumference on my own,
there was about 2,5cm less rear then front. Calculated this makes more than 1% difference.
This makes the system think that there is always wheelspin in the rear and engages the front drivetrain much harder as effectively needed.
Together with the sloppy tranny bushings you get a nice plop.
The xdrive system also reacts to this difference and tries to compensate, but mechanically this is not possible as there is no center diff.
My car was almost undriveable, when xdrive engaged the front pulled more than the rear was pushing and reacted unpredictabely with lots of understeer.
Take a wire an test on your own,
then get the correct tire measure.