I have run into this problem, and ran a few test to see if it was an inductive kick back like that which use to happen to ceiling fans, and after five times letting the washer trip the GFCI, the scope showed about a 1.8kv kick right at the time the washer water fill valves kicked off, this is also right when the GFCI tripped, I don't have the interface for the tech-tronic scope to upload the trace to the computer, but it does have capture for events.
What I did fine out was changing the GFCI to a leviton stopped the tripping, the GFCI that was installed was the cheap Menard's ones in the red box's, newer GFCI's are supposed to have electronics to reject inductive kickback, but there are these cheap made in China ones still getting past this UL requirement.
So if you get called on this problem and find a washer full of water but not running, then this is what is happening, it will trip from an inductive kick back from the fill valve being turned off, leaving the washer full of water, (unless the home owner resets the GFCI and finishes the load)