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I'm not fond of soap made/marketed for/to campers either. Doc Bonner's, Camp Suds and the like disappoint and interestingly enough, I can't find any reference to soap in either the 2009 QP regs or in the following PDF for the BW:
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I'm going to go out on a limb and suggest that LNT principles often have more to do with simple aesthetics and perception than anything else. We're not talking phosphates here. It's just soap. Right? The water is soft, you don't need much. See how little you can use since the less you use, the less rinse water you need to warm and lug around too.

Use what works for you ... well inland ... just don't leave a ring. If you want to be extra kind, you could avoid deodorant soap as it is designed to kill bacteria which could help the stuff break down??? Then again, something that has a better chance of allowing you to skip a day or three or seven might be a good compromise. Go easy on the conditioner if you are so inclined too.

I expect rinsing off deet is wishful thinking as it's absorbed rather quickly. Try thinking of it as a base layer. Never met a woman who didn't prefer a sun shower over a lake rinse.