X5 50e owner here. While I don't have a solution - I'll share my experience regarding this issue. My 2013 Audi had the same "feature". I asked my dealer to turn this off and I was told that this is a safety feature and can't be turned off. My reason for asking that was that the ICE engine would shut down and along with it the heating/cooling and it was an annoyance.
Fast forward 10 years and now I also have a Volvo c40 which is full electric. First time I sat in it - I couldn't find the on/off push button, to be told that the car has none ! You just walk in, the car switches on including the climate. The motor doesn't starts even when you engage the drive or reverse. Its only when you release the brake that the motor get energized. You put it in park and just walk away and it shuts down. Took me couple of days to get adjusted to the new paradigm
X5 PHEV falls in the middle I think. When you push the start button, it starts on battery including the climate I think, ICE doesnt starts unless you push some button on the drive to make it start while its in parking. For the same safety reasons and also to conserve the battery it shuts down the car if the driver exits the car. Its still an annoyance to "push" the button to start but its not like it kick in the ICE engine for anything. I have not tried it yet but you can start the climate using the phone app while the car is parked if that's the only reason to not have the car shut down.