An energy plan should be a part of prepping in my opinion, and would help in the clothes washing area. Jack had a pretty cool show last week on solar backups and a washer could fit into the systems they were discussing. Most washers are 110V and could run off a generator or, better, a battery back up system tied to both solar panels and the grid. The new models won't kill you on watts either. Assuming a well system in your energy plan and a septic system (this wouldn't work in the city or suburbs) you could make the washing machine work. If you were using solar you would want to do it on sunny days when the batteries are fully charged so you don't run an energy deficit there.
This won't work for electric dryers that are normally 220V and less likely to work on a backup system unless you set some double pull breakers in the subpanel and have a transformer that can do both 110V and 220V (I'm sure they are available, I'm just not familiar with them), plus the electric dryers probably use a ton of watts to dry clothes. Fortunately, clothelines work just fine!