I always turn my AC off before shutting down my truck. Not because I think it will hurt it, but because I am set in my ways. When I start my truck I have a set order I do everything in. I get in, and press the clutch, and brake. Verify that the transmition is in neutral. Put the key in, and start the truck. Then I turn on the lights, radio, AC/Heater. Release the parking brake, put it in gear, and drive off. When I stop I alwasy take it out of gear, put the parking brake on, turn off lights, AC/Heater, and the radio. Then I turn off the truck, release the brake, then the clutch.
Nothing to do with it damaging it, just the way I do it.