Well I bought a "pure" sine wave for about £150 for a 2KW inverter - I don't think it is pure sine wave like the beautiful £1500 victron which I foolishly sold with my last boat, but it is not square or modified sine either, I think it is a "simulated pure" or something where the pattern is simulated by increasing or reducing the voltage.
I haven't tried a washing machine, but it runs phone chargers, laptop, vacuum cleaner, and microwave which traditionally give these things trouble.
It is certainly possible that a sophisticated washing machine has more computing power and is more prissy than my laptop, in which case maybe get a twin tub as Bod suggested, or spend a couple of thousand on a decent inverter.
I suppose I'll have to lug the washing machine onto the boat now... (-: