This seems to be the intersection of two maddening (and long standing) bugs:
1) mute does not mean mute -- it clearly should.
2) volume control does not work properly. In fact, if you are wired into the car stereo, the volume resets to MAXIMUM each time you launch the app. The slider retains the proper setting, but the actual volume is MAX. This can be reset by opening settings, going to sound, sliding the volume slider al the way to max, then sliding it back where you want it (perhaps zero to get around bug #1).
I have to do this every time I get into my car, or the thing shouts at max volume over my music. It's awful. Please fix!
Also, while I am ranting, please make Waze shut off automatically after I finish my drive like it did under ios5. If I forget to explicitly shut it down, it kills my battery.