On a gasoline vehicle, the immobilizer is automatic and there is nothing to touch. If you don't have the key in it, the vehicle won't start. Don't see why it would be any different with a diesel.

Really? You ever tried to push start a Diesel in gear???
If it worked for you then good but the last time I tried that
there was no bump start of the vehicle in gear.

In fact to achieve the start you have to get some
good speed like 20MPH for a manual shift not a bump imo.
For an automatic it may be possible but getting enough speed
to achieve ignition of diesel fuel? I think in a BMW with an
auto tranny your asking for trouble.

Additionally The question I would ask is the diesel fuel pump electrical?
If it is then your dead in the water. No matter how much pushing
you do that pump aint gonna work. No fuel no start period.

Yes, you can bump start a diesel in gear, and yes I have done it, if you have electrical power for things like fuel pumps. Bump start refers to bumping the engine over using the inertia of the vehicle. Yes, you will need sufficient speed. Your post suggested that the vehicle could be immobilized by disconnecting the starter motor circuit, and I commented that that wouldn't be enough to stop the vehicle, ie to immobilize it. If you just interupted the start motor circuit you would still have power to the ancillary circuits (like the fuel pump)

You can't bump start a BMW automatic (or any recent automatic, going back many decades) because they don't have rear pumps. If there is a pump on the output shaft of the transmission like early automatics had, you can build hydraulic pressure and then start it, but these vehicles don't have rear pumps.

Since BMW built both manual and automatic transmission X5 diesels, it would make no sense to me to immobilize the automatic models by disabling only the starter motor, and letting the manual transmission models be at risk of theft.

Well I guess times have changed. In 1976 I owned a Peugoet
diesel. I owned it for 10 years and no one was ever able to start
that vehicle with a "BUMP" even going down hill and it didn't
have an electric fuel pump.

But I guess if someone is going to steal a BMW Diesel these days
and they can bump start one with a manual transmission
and an electric fuel pump with no key by pushing it down the
street at 20 MPH then they can have at it.

I guess if they really want the vehicle that bad it's possible.
Somehow I just don't believe it's very plausible. But who knows
stranger things have happened.

BTW Your right BMW Diesels don't have ignition immobilizers
I believe they might have engine immobilizers.