If white wire of that AFGI circuit makes any contact with any other
white wire of any other circuit, then circuit will work just fine with
any other breaker and AFGI breaker will trip.

That AGFI circuit cannot share a common neutral with any other
circuit. And safety ground wire cannot make accidental contact with
the white wire until all meet in the breaker box.

To avoid other problems created by defective appliance (ie. a switch
that sparks when disconnecting), safety grounds of both circuits should
remain separated. Does the refrigerator switching on or off create
popping sounds on an AM radio not tuned to a strong station? Does only
refrigerator cause tripping? Does another high current device
(electric heater, power saw, vacuum cleaner) not cause same tripping?

These suggestions made only because it is not 100% clear what is and
is not inside common boxes and shared with other circuits.

Assuming the AGFI is working properly, then something inside a common
electrical box is making electrical contact between circuits. A
problem never detected by conventional circuit breakers.

Ed wrote:
The fridge is on a completely different circuit. When the AFCI circuit
trips, the refridgerator stays on

If the feedback surge can be felt on a different line, then in general,
that would make it very difficult to find the cause of the afci trip.