The Muse companion app requires access to the audio system. Just like you can't use Pandora and Spotify at the same time, you can't use Muse and another music app at the same time. You can, however, use Muse with other non-audio apps such as Maps, Waze, etc.
You can enjoy music with Alexa in the Muse app with Amazon Music, iHeartRadio, TuneIn, SiriusXM and Pandora. Spotify is on the product roadmap.