Is there any way to 'turn off' the sync of saved songs between Classical app and Music app?

I heard that Classical app had been their own library independent of Music app. But when I save a song in Classical app (Tracks), this song appears in my Music app (Songs).

I think this is unpractical; the reason to have two apps is that when I want to hear classical music, I go to the Classical app, and for the rest of my music, I go to the Music app. Rarely I want a kind of 'Mix' with both styles.

Thanks!