As with so many things, there isn't one right answer.
1. In areas with very high environmental costs to heating water, cold water solutions are necessary. (And hopefully, people will plant coppicing trees/shrubs and build a rocket stove to heat a pot of water on, for the future.)
2. In areas where drought is a severe issue, people may have no choice but to use a low water, higher soap approach to the problem of getting things clean. (and hopefully plant tree/shrubs to help reverse desertification.)
3. In places where people cannot use greywater systems and know that their water is going straight into streams and rivers, avoiding soaps/detergents that contribute to algae formation is *really* important for the environment as a whole, but many people are not so good at looking past their own front door without nudges from people higher up Paul's eco scale. In those situations, high water/low detergent/soap are likely the best compromise.
4. Within all of these options, "reduce" is step one. For example, we use colour-coded cups for family members and mostly drink straight water. I'll easily use the same cup repeatedly for 1-3 days before I consider it dirty enough to be washed. If I have just a sandwich for lunch, I'll often use the same plate for dinner by just wiping the crumbs into the compost with my hand. I *hang* my bath-towel after use - after all it got used on a "clean me", but I know people who wash their towels after every use - letting something air-dry kills the vast majority of micros without any soap or water getting involved, leave a towel in a damp heap and laundering becomes necessary.
It all comes down to the basic principles of Permaculture: observe, adapt to your situation, identify a problem and work towards solutions!
Soap can be made in a low tech, traditional, eco friendly way. They make olive oil soap in the middle of North African desert countries. Soap should not be our enemy, I think..
Making soap requires energy, but burning a bit of kindling for a batch of soap that will last you a year isn't that bad, I think.
Dish washing without soap really needs old fashioned scalding hot water and scrubbing. Boil water pour over greasy dishes in a tub, let sit a bit, and scrub away.
Here's how artisans make olive oil soap in North Africa. You CAN use this stuff to wash dishes, hands, everything. My wife refuses to wash lingerie or socks with anything other than either French Savon de Marseilles, or a traditional Olive Oil soap like this...
I didn't read the whole thread yet; sorry if this was already posted.
The Viking system might be good for you. I learned it when I stayed at the Viking Village at Lejre Land of Legends:
We passed the dishes through 3 basins of water in order: (1) a warm water basin with a scrubber, to remove the food stuck on; (2) a cold water basin where you rinse off the rest; (3) a hot water basin to disinfect it. Then we let them drip-dry on a rack.
The dishes and spoones were all wooden, so maybe this method only works for wooden items.
The stew was cooked in a big metal cauldron hung below a tripod over a fire, and I didn't see how they cleaned that.
For dessert we ate raspberries with cream (which had been hand-churned). The dish washing system cleaned the grease off perfectly.
Oh, and before going into the first basin, I would try to scrub off stuck food particles with a handful of plants (such as a comfrey leaf).
Permaculture dominated the world until 50 years ago. World re-domination of permaculture is the only way forward.