Shopkick's sound profile uses the main media sound on your phone, just like your music player. Because it can't play two sound profiles at once, your music will turn off when Shopkick opens.

To turn off Shopkick app sounds, tap the menu icon to access the left menu and scroll to "Settings." Disable "Sounds" (on iPhone, slide the toggle off; on Android, tap "Sounds" to uncheck it).