Hey tophdna,
Thanks for reaching out for help in the Apple Support Communities. I can see from your post that you're unable to disable the repeat function in Apple Music in the new Music app in iOS 10. You can find information on how to use Apple Music in the new Music app from the link below.
Use Apple Music in the Music app
Up Next, Shuffle, and Repeat
Also on the Now Playing screen, you can rewind, pause, or fast forward a song, control the volume, read song lyrics, and more.
Swipe up on Now Playing to show your Up Next queue, which lists all of the songs that you’ve selected for playback.
Drag songs with to rearrange the order, or swipe left to remove a song that you’d like to skip.
Tap to the right of Up Next to shuffle the songs in a playlist or album.
Tap once to play an entire playlist or album on repeat or twice to repeat one song. Tap a third time to clear the repeat.
If you have repeat turned on, you might not see .
Hope this helps.
Cheers.