I wouldn't personally want a load of chicken poop and potential rodent contamination in my washer -- especially because the water-saver features on modern machines make it difficult to get heavily-soiled items clean. But if you have the appropriate equipment. :)
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That's a clever temporary solution, but over time those blankets will mold and attract vermin.
If you need sound insulation, dense vegetation appropriate to your climate between the coop and the neighbors would be a better option over the long-term. You can add your general...