I played this game a few months ago with the disc and had no problems then. I take very good care of my discs. Now months later I can't play the game as my xbox doesn't recognize it. It isn't the disc drive as I am still able to play GTA V which I have only on disc. I also started playing Doom again recently. As of this post I'm currently attempting to download the free trial, hoping I can at least get to play one last time. Anyway, for some reason, my consol won't recognize this specific disc, which has had good, clean runs on this xbox one.
Have you tried to clean the disc, using a lint free lens clearer type cloth move from the center straight to the outside (in a straight line) NOT circle movement. Destiny 1 discs should be cheap to get from a place that sells them , as used discs usually have a guarantee that they work or they replace it. I still use my Xbox 360 (dvd) and Xbox 1 (bluray) Destiny 1 disc every week.