Yes, I'm pretty sure mahogany will turn dark from soap. Bummer -- it's very pretty.
Cherry, oak, redwood, cedar, and walnut, as well as mahogany and many other tropical woods will darken. Pine, maple, and poplar are not especially pretty but are safer bets for use with soap if you don't want discoloration.
If you think about these different woods -- the darker the wood, the more likely it is to not play well with soap.