I had restrictions turned off on my iPhone 11 Pro Max running iOS 13, yet I wasn’t able to play/download tracks marked “E” in Apple Music.
On searching google I came across a work around
Go to iTunes Store (Pink icon).
Search for an explicit song and click BUY (you don’t have to actually buy it).
Pop-Up asking for permission to ALLOW explicit content will pop up.
Now APPLE MUSIC will also allow the Explicit content