In a washing machine you wash clothes in heavy mode then it moves a bit. Then it is doing work with internal force. Then does it violate that any work can not be done with internal force?
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Friction: As sku pointed out in a comment, friction plays in important role here: it makes Earth part of the system.
As the internal parts of the washer move, if the device were floating free in space, its body would also move due to linear momentum conservation. But the device is actually sitting on Earth on a floor which is not frictionless: so whenever static friction can't be high enough to stop the body from moving, it'll move.
Of course, for you to observe a net displacement after the machine cycle is over, there has to be (supposing the machine starts and finishes in the same configuration) a source of asymmetry. This is usually provided by the machines' foot and/or floor (unevenness, inclination, ratchet effect, etc.) or by the drum not being symmetrically loaded (the clothes can clump mostly on one side of the drum) and therefore not roting uniformly.
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