Just want to post what I have found with iOS 10.0.2 and Music Up Next list...
If you are still having trouble with removed songs reappearing back into the Up Next list, I seem to have found a way to get all the song removed from the Up Next list to stay removed and not "magically" return when the current song switiches to the next song.
After removing songs from the Up Next list - change the order of at least one song in the list. That seems to lock-in the "remove" changes that get ignored when the current playing song changes. Don't know why???
I found this by trial and error after noticing the removals would sometimes return (and sometimes not) when the song changed. I narrowed it down to moving the order of at least one song to get the removed songs to stay locked out. If the only edit I make is song removals, without changing any song's order, then the removed songs return to the list when the current playing song changes.
I'm not sure why Apple chooses to make removing a song from the Up Next list a two step process for each song (swipe Left, then hit Remove) but when you want to remove a whole bunch of emails from, say, Mail you can do it in one big batch at a time with an Edit/Done window. The Up Next list should have an Edit/Done option like any other list within Apple.
Anyhow, that's what I've found - hope it helps.
Q.