That is the first I have heard of that problem. Questions: Did you try and run the washer just on the inverter? Does your inverter have a maximum 110v draw setting (maximum power it will take from shore or the genset)? If so at what level is it set? Unintentionally we set our maximum draw too low one time and the bypass was unable to power the tea pot.
Yes, it was a real head scratcher. It's been several years now, so I'm going off memory which is dangerous but.... I think the kicker was that the washer wasn't even wired to the inverter. The inverter powered a select set of circuits, and the washer was not one of them. So washer load and inverter capacity never interacted with one another. They were just side by side loads on the same shore or gen power source. So it could only be electrical noise (radiated or conducted) that was tricking the washer. And the washer failure mode was very odd too. When you first start it, it goes through a short cycle to be sure the drum is pumped dry. It would remain stuck in that cycle until it errorred out. The error code said the drum was both empty and full at the same time, so some sort of sensor malfunction. Turn off the inverter (remember, it's just a side by side load, like running the TV at the same time), and the washer would work fine. I replaced all the relevant parts as my expense and to no avail. I also experimented with ferrites on the power cord, but no joy.
My final conclusion was that without a scope I would never figure it out, and I had long ago thrown away my 100 lb, tube-powered Tektronics scope.
I have encountered two other similar problems, but these are sensitivities to running on a generator. One was the electronic igniter (the spark spark spark lighter) on a gas stove. It would not go click click click when the house was running on the generator. Definitely not a load problem since the clicker draws only a tiny amount of power. It cause quite the surprise on Thanksgiving when we discovered the oven had not relit in the past 3 hours and the turkey was still raw....
I've got another such issue currently with a modern gas boiler. It's a Buderus modulated super efficient burner that heats my barn/shop. When my generator is running, it errors out. It lights, but the flame detect circuit doesn't agree and it shuts down. After a few attempts it locks out and requires a manual reset - something that does not go well with unattended operation. I ended up building a lockout circuit to keep the boiler from firing when the generator is running. The shop building is super insulated with lots of thermal mass, so the temp only drops a degree or two over an 8hr generator run, so it works OK.
One irony here is that I've had much better success running devices off inverters than off generators. I don't think I've found anything that doesn't work off a sine wave inverter, where I have a handful that don't work off of generators.