How can a compressor noise, or any normal noise emanating from a car, be "embarrassing"? This must be the first AC compressor in history that makes someone feel ashamed. That's not the response I had, not by a long shot. I've had my car for over 9 months. The compressor is loud because there is no engine noise masking the compressor. There is nothing abnormal about the noise itself. Cars make noises. So do EVs, for that matter. Just because our cars are electric doesn't mean they will always be silent in every circumstance. Cars make noises.
The first time I heard the AC compressor, I thought "oh hey, that's the AC. Cool." I never assigned a negative emotional value to that noise. It's a normal noise. Just like the vacuum pump coming on when you tap your brake pedal. Or the car making a similar noise while it re-levels itself when you exist. Living in AZ, I'm thankful the Model S has such a powerful AC.
I've never heard the AC of an ICE be anywhere near as loud. To me, this isn't like the vacuum pump for the brakes or some other random noise -- it's so much louder. Heck even driving an ICE is less disturbing to listen to than the racket this AC puts out. It's not horrible inside the cabin (it's not great) but it's pretty crazy outside the cabin. The pitch / makeup of the noise is perhaps the worst component (versus the decibels involved).