I was told by a friend, who is an airline pilot, that switching off my car's air-conditioner is part of the correct shutdown procedure. Is this true?
Certain specific steps are necessary when shutting down an aircraft. As you can imagine, a car is a very different machine.
Apart from parking the vehicle in a proper place, shifting the gear lever to P (in the case of an automatic transmission) or first gear (in the case of a manual transmission) and pulling up the parking brake, there is really no other procedure to perform.
With most cars these days, the air-conditioning system, even if its switch is in the "on" position, will be activated only when the engine has started and is at least at idling speed.
Not turning off the air-conditioning when shutting down the engine will not cause any electrical or mechanical damage.
Only with old cars - mainly those more than 20 years in age - is the compressor activated the moment the ignition is switched on. This causes additional load to be placed on the starter-motor, which is why it is advisable to keep the air-conditioning off when starting the old car in question.