I actually don't think the bug is solely related to re-adding the songs that have been removed from the "up next" queue. Rather, I think the bug is, when playing music on shuffle, after every song that completely plays through, Apple Music reshuffles the entire "up next" queue. This causes 2 primary issues that have been discussed in this thread.
1. Songs often get repeated after recently being played because the order has been reshuffled and previously played songs reappear as up next.
2. Songs that have been removed from up next get added back to the up next list once the entire queue gets reshuffled after a completed song.
These issues are very annoying but far less intrusive than my Google Play Music issue of 500+ songs not appearing in my thumbs-up playlist. Regardless, hopefully Apple can get this squared away when they release 10.2. I hear they are also bringing back the star rating system (this was posted by a Beta user 🙂 ).