Air conditioner stops working when the engine roar begins. What is the culpret.

The "engine roar" is from the electronic, thematically controlled radiator *cooling fan clutch* spinning the fan faster to cool the overheating engine .. A/C compressor will turn off when engine temperature reaches/exceeds pre-set thermal limit.. When the temperature gauge went to hot, the engine 'was' actually hot! .. Possible failing engine thermostat or low coolant level... Hands-on testing required .. Also possible trouble code(s) stored, suggest scan test.

I wish I had another option. I have replaced the thermostat and when it would overheat the roar would happen so I replaced the Cooling fan clutch and the roar is still there with no other issue that I'm aware of so I am literally lost and honestly running out of options/money