These systems are not directly related and in fact they don't even share a common component. So that means this is a software issue where the changing of the fan speed is telling the HVAC module to tell the PCM to shut off the compressor.
The way it works is when you press the A/C button on the HVAC module, it sends a signal to the PCM that there was a command for A/C and the PCM turns on the compressor.
So I suspect the issue is the HVAC control module. The way to confirm this is to test voltage on the A/C request wire (light green) when you have the A/C on and it is working. Then change the blower speed and see if that voltage goes away. If it does then the issue is in the HVAC module and the PCM/compressor are just responding to what the HVAC is telling it to do.
Please see the info below and let us know what you find or if you have questions. Thanks
Images (Click to enlarge)
Tuesday, July 6th, 2021 AT 8:49 AM