Finished leather is acidic in nature. It is why the leather fibers form bonds with the tanning agents and remains flexible. Any sort of natural soap is highly alkaline relative to where finished leather is at its optimal point. Exposing leather that's finished with a pH between 3 and 5 to any soap which is has a pH of generally around 9 shifts the amphoteric protein fibers ionic negative, which makes it stiff and causes tanning agents to leach out of the leather.
The most important thing you can do for shoes is keep them clean and acidic.
Thats probably why the boot.com link says to use glycerin soap. The pH of glycerin is almost neutral, a bit acidic: http://chemistry.stackexchange.com/questions/7838/what-is-the-ph-of-1m-glycerol
Now obviously the rest of the ingredients may change that and it also seems that the Pears soap pictured has undergone some changes in formula after 2009 after staying the same from 1807 to 2009. Shame that is.