I'm using MacOS Catalina 10.15.3
I have two Apple IDs (old and new). I tried to use Family Sharing between old and new Apple ID but it did not work as I expected. To test I've signed up with the new ID in Apple Music. I switched back in Books, App Store via System settings -> Apple-ID > "Medien & Käufe" (German) and it works fine there. However in Music it somehow doesn't work.
Every time I want to change to my other Apple ID, the login popup appears in Music showing my new Apple ID. I then enter my old Apple ID into the Apple-ID field and the correct password. The login works but then right afterwards the login popup is shown again with my new Apple-ID.
How can I logoff in Apple Music or delete the "new" Apple-ID?