IIRC, regular old fashioned soap is made from fats mixed with lye. Saddlesoap like Properts is compounded much like regular soap--it's supposed to be used with water...at least enough to work up a lather. And that means a very wet sponge or running water. The glycerin bars are intended to work up a lather as well. Lexol-ph is formulated very much like ph-balanced baby shampoo (which makes a fine leather cleaner, BTW). Again lathering and rinsing is indicated.
It is not automatically harmful to rinse leather with running water...lots of processes in making shoes or working leather are entirely dependent on getting the leather wet. Shoes, however, tend to have inconsistent areas of absorption after they have been worn awhile simply because of all the polish (wax) build-up. The water will not by itself have any deleterious effects esp. if the shoes are conditioned immediately after washing/rinsing--while the leather is still wet. The real problem is water stains that may result from heavy absorption in one area and less in another...again conditioning can go a long way towards preventing that.
If you're concerned, again using a very wet sponge is a good solution.
But the bottom line is that leaving the tallow or glycerin residues on shoes is not good. If nothing else, it will collect dust and grit and accelerate cracking.
And you can't get either a high or a long lasting shine over grease.
When you get right down to it, it's worth remembering that saddlesoap was formulated for saddles.
Thanks for the response, as always!
I use Fiebing's Saddle Soap Paste: http://www.fiebing.com/catalogue/soaps-oils/?product=97 Not because I'm loyal to it, but simply because it's what my nearest cobbler carried way back when I bought it. I use a wet natural sea sponge to work up a lather and apply it. Once it's dry, I wipe with a cloth and then buff with a brush. Like I said, it's really just one particular belt that I regularly use it on (a thick, heavy, casual leather belt that is usually worn with jeans). I have a pair of saddle shoes that I used it on for a while, made from Horween's Dublin leather, but I quit because I didn't like the build-up that started developing around the stitches. However, that was happening by following the instructions on the back of the tin, which doesn't say to rinse off the leather.
If I ever have cause to use it on them again, I'll certainly make sure I rinse it better, and I'll do the same with my belt.
One follow up question to your response above. Do you always recommend conditioning while the leather is still wet? How about in the case of shoes that get saturated in a downpour? Most of the information you find out there recommends letting them dry in the standard method (on their sides, away from heat, stuffed with newspaper, etc.) and then conditioning/polishing after they have thoroughly dried. It actually makes perfect sense to me that conditioning them while wet would keep the fibers properly lubricated while the water evaporates. But again, that's not what you generally find recommended "out there." Not saying I believe everything I read, of course.