Speaking as a long time backpacker, whatever kind of soap you use the most important thing is to not contaminate water sources. Wash yourself and dishes well away from lakes or streams. 200 to 300 feet is the distance generally agreed upon, even though that seems like a long way to carry water. Discard any dirty or soapy water on the ground, not into the water source. Even soap labeled biodegradable won't break down immediately. I often carry a Sun Shower or Solar Shower with me. When I get to camp I fill it up, let it warm in the sun (how long depends on the weather), and sneak off into the woods for a nice (spartan) shower. If I'm traveling light or the weather is cold, I heat up a pan full of water on the stove and take a sponge bath. You'd be surprised how little soap it takes to get clean, and lather has nothing to do with how clean the soap gets things.