I had the same problem and I figured out how to fix it...
On your iPhone, open Apple Music and click the “Listen Now” tab. Go through the steps of choosing genres and artists you like. Make sure this task is completed in it’s entirety. Now go back to CarPlay and click over to Library then back to “Listen Now”. This solved the problem for me.
Apple certainly needs to write better handling for this “glitch.” Perhaps a friendly message that reads, “Please launch Apple Music on your iPhone and complete the setup process on the “Listen Now” tab.”
Hopefully this resolves the issue for you guys. Let me know :-)