How do I clear a drain pipe clogged with dried soap?
Moving water, preferably hot. If you can get a small flow that
doesn't back up then it will dissolve away easily.  
Environmentally safe degreaser/cleaner, I prefer Simple Green
Baking soda and vinegar, it will clean almost any small clog. With something that dissolves easily like soap, the extra air bubbles produced will help getting it clean with less passes as well.