I have been camping all of my life (and that is a lot of years, and a lot of camping trips), and I have never seen a campground that would not allow dumping dish water. Many campgrounds even have a grey water dumping site in each campsite, or at least centrally located. Have to give this some thought, but right off the top of my head, the privy, or your five gal can thing are all that come to mind...
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OBG