Update. The GFCI can also trip when the power supply was put on the load side instead of the input. Here the input is open. So it's not current inbalance in the sense coil, please explain how can inductive kick can trip it when ac supply is put in the load side.
Here is a GFCI youtube video that continuously trips when you use water shaded pole motor. It doesn't trip on other appliance, The motor was surrounded by plastic, glass surface and glove hands so there is no way current can escape. Can the tripping be caused by inductive kick from motor inducing capacitive coupling inside the circuit? How do you refute this theory?