Apple Music overrides Synch Only Ticked Songs and Skip When Shuffling

Since getting Apple Music, all my songs are now on my phone. Every single one. I very carefully curate songs in iTunes that I want on my phone and Apple Music completely ignores that. It shuffles every song, including musical soundtracks which I deliberately set to skip when shuffling because nobody wants one random Hamilton song just popping up.

How do I get my Apple Music to do what I want it to do, which is only play synched songs and ignore certain tracks when shuffling?