A/C problems
 

I have a 2002 Honda Civic manual transmission. The air conditioner has been cutting out recently only when I put the car in gear, any gear except neutral. It will resume cold air when the transmission is in neutral. I've done some research and the closest thing it might be I think is a faulty thermal protector on the compressor. Any ideas?

Compressor intermittently failing to engage is usually the clutch gap or a bad relay. Clutch gap can be adjusted with the compressor on the car and the system charged. If the space between the clutch plate and the pulley looks like more than about 0.025 inches, you should reduce it.

There are several relays in the relay box of the same type, so just swap the compressor relay with one for a system you're not using right now (the rear defogger for example) and see if that helps.

I think that being in neutral is just a coincidence because it doesn't make much sense. The electrical system of the car has no connection to the manual transmission. There is logic in the ECU that will cut out the A/C if the engine idle rpm goes too low, to prevent stalling. That could happen on an automatic car.