If washers have variable speed drives it is very likely high frequency leakage causing the tripping.
First time I ran into this, the manufacturer actually did address the issue but their solution happened to fail. What they did was to run the equipment ground to the motor through a "door switch" that is held open when the back cover is installed. That interrupts the path for the leakage, but closes circuit should back cover be removed. The unit I was working with had plastic mount for this switch break so it closed the circuit even though cover was on.
One quick and easy thing to do is plug the machine in with one of those two to three prong cheaters and see if it works that way. This leaves EGC open so it can't return the leakage. Not a good idea to use that as a solution to the problem, but if GFCI holds it does tell you there is leakage to ground that is causing it to trip.