In some places it's encouraged. Just run your gray water right into a bucket and pour it into the bushes. In any campground where there are tents it will be fine. Our camper has separate hoses so there is no black tank crossover. And really, we usually do the dishes outside anyway. Makes sense if you cook outside, just do the dishes outside too.
The exception is in bear country. Then the food particles are a concern. When we are camping in Alaska we use disposable stuff and it either gets burned or goes in the dumpster at night.