DIAGNOSIS The microwave is drawing a sudden, high current that's exceeding the GFCI's sensitivity. This is often caused by a minor internal arc or a failing component, most commonly the high-voltage capacitor or the magnetron itself.
FIX First, rule out the outlet. 1) Unplug the microwave. 2) Plug a different, high-power appliance (like a toaster or kettle) into the same GFCI outlet and turn it on. If it also trips, the outlet or circuit is the issue. If it doesn't trip, the problem is in the microwave. For the microwave, this is not a user-serviceable fix. The unit needs to be examined by a qualified technician to test and replace the faulty high-voltage component.
IF THAT DIDN'T WORK If you've confirmed the outlet is fine, do not keep trying the microwave on different circuits. You risk further damage or a safety hazard. The repair requires disassembling the unit and safely discharging the high-voltage capacitor, which stores a lethal charge even when unplugged.
HEADS UP Never bypass a GFCI outlet for a microwave. It's tripping because it detects a potential ground fault, which is a shock or fire risk. This is a "stop using and get it checked" situation.