Old post from the Chief:
There are two different AC systems in use on the ship. One is like a window AC unit at home, that merely takes the cabin air and cools it while recirculating it back to the cabin. This is what is controlled by the cabin thermostat, and by the balcony door interlock, if fitted. This system is designed to recirculate 80% of the cabin's volume each hour.
The second AC system is the one that is affected by the balcony door being open, and that affects the cabins around yours when you leave the door open. This system is not controllable from the cabin, and can not be shut off. This system is designed to bring fresh air into the cabin, about 20% of the volume per hour, and is balanced by the bathroom exhaust vent, which removes about 20% per hour. This system takes outside fresh air, cools it in a large air handler (in those big white spaces down the middle of most cabin decks), and supplies this air to all of the cabins in a particular fire zone (between those pesky doors in the passageway) for one or two decks, meaning one fan and cooler handles 30-50 cabins. Now, this air is sent to the cabin at a higher pressure than normal HVAC systems, for one reason. This "overpressures" the cabins, forcing any leakage at the door to go out into the passageway, not the other way around. This prevents any possible smoke ingress to your cabin in an emergency.
Now, what happens when you open your balcony door? You replace the 2" diameter bathroom vent, and the 3/4" x 3' crack under the door that maintains the pressure balance in the cabin, with a 3' x 6' opening to outside. This immediately drops the cabin pressure to atmospheric, and the fresh air supply AC system sends all of the air to your cabin trying to rebuild the over pressure. This means that the other cabins lose much of their supply of fresh air (cooled), and also their overpressure safety feature, and now air is drawn back into their cabins from under the door, from the passageway (warmer). Therefore, the other cabins in the zone lose some of their AC capacity, and start getting warmer air supplied to the cabin.
How can you tell if this is happening? Real simple. I used to do it daily when I worked on cruise ships. You walk down the passageway, and listen for the air whistling under a door. 99 times out of 100, I would find the balcony door open in that cabin. Also, if it is your cabin with the door open, when you open the door to the passageway, you will create a wind tunnel, that blows everything out of your cabin. It doesn't do this when the balcony door is closed, so the door being open obviously has an effect on the AC balance in other areas than your cabin.
Your humble opinion may think it is BS, but I've worked on ships for 42 years as an engineer, 35 as Chief Engineer, and I have intimate knowledge of shipboard AC systems. Yes, there is a proven effect on others from having your balcony door open, and I've had to deal with it constantly over the years I worked cruise ships, when we would get whole banks of cabins complaining about their AC.