The first post I answered why I don't like liquid soap for showering. But it's entirely because I like to stand in the spraying water the entire time, and liquid soap goes away instantly.
As for your deodorant question, I've been using this for a little over a year and it's fucking awesome. I don't have BO any longer, and that's busting my ass in the sun and sweating the entire day. It's glorious.
Amazon product ASIN B00XV5W1IKIt's a smooth cylinder of salt. You wet your pits, crotch... hell, anywhere that gets funky when you sweat a lot. Then just rub it on a lot. It's a bar of salt, so you just keep rubbing it until you think it'll be good. The water slowly dissolves the salt it's touching, which is how you get "covered". I don't suggest wetting the salt itself down, because every time you put it away, the water runs down the cylinder and weakens the base where it sits. I've had 2 bars fall out onto the bathroom floor when I flipped it over to do my pits, and when it hits the floor, it explodes into a hundred pieces. Now that I've swapped to wetting my pits directly, the base remains solid for the long haul.
You'll still sweat. This is NOT an anti-antiperspirant. But the salt prevents bacteria that live in your pit hair from reproducing when you start to sweat. And it's the bacteria that causes you to stink. Nothing more. Kill the bacteria, kill the smell. Problem solved.
EDIT: I apply it by wetting my pits right after I finish up with my shower and dry off. Then go to bed. When I wake up, I'll soak my pits a bit more and wipe the "old" salt away and re apply it, just to be safe. That's enough for me. And this single stick (cylinder) will last a year. It's pretty awesome for costing around $7 per.
