In our 8.7.0 update, we changed the way the "Built-in Music" option works so now it only displays playlists where all the songs are downloaded and don't have DRM.
DRM means "Digital Rights Management" and is used to encrypt songs to prevent piracy. It was used on songs bought from iTunes for a few years, and also applies to some songs synced via iTunes Match. Apple has always prevented us from playing DRMed songs.
In the past, we would skip over songs we couldn't play, but this was buggy, so we now hide playlists containing those songs.
So: if you update your playlist to exclude songs that aren't downloaded or DRMed, that should work!
If you are unsure whether tracks have DRM, you can check out file types by opening up iTunes (or the Music app) on a computer, going to View > View Options and enabling 'Kind'. This will then show you the type of file each track is. generally songs with DRM will show up as 'Protected AAC'.