Parking next to the 'community spigot,' you have to expect a fair amount of traffic. It shouldn't be a surprise you will be sharing that space with others.
I don't see the big deal with dish washing in a tub and then dumping the (very, very small amount) of water.
IMHO, society does MORE damage to our environment by taking millions of gallons from one area, contaminating it with chlorine, fluoride, and whatever else, and dumping it miles away for many generations, then wondering why we have droughts and floods and water pollution :R
A possible 'fix' for the tent campers is a gravel filled drain basin next to the spigots for dish water. A splash of bleach regularly and an occasional dumping/refill of the basin would be all that is needed to avoid food/grease over-saturation. I'm sure it could even be made as an attractive planter. Simple.
It seems short-sighted to make rules preventing tent campers from washing their dishes (yes, they DO need to eat!) and not make other accommodations. Either let them dump in the woods or other suitable area, or make facilities available and CONVENIENT/nearby.
As for doing their 'business' behind the trees? Smokers exhale FAR MORE TOXIC and polluted material with each puff than a camper relieving himself 3 or 4 times a day. Oh- and that is not carcinogenic ;)
Really, some people worry FAR too much about OTHER people.