If you simply want to create UWP projects for the Xbox, you only need to register for the new Xbox Live Creators Program
For this you don't need the XDP or access to the Xbox branch of MonoGame, just the Windows 10 UWP templates. (targeting the Anniversary build 14393+)
I did a video session on this there:
If you then want to go Full native, as @cra0zy states, you will need to apply to ID@Xbox with a pitch for your title. I recommend starting with UWP, then look to ID if you are hitting the perf wall and have a project you can demo to them.
Remember UWP, gives you access to all Win 10 platforms, from Desktop / laptop / mobile / xbox and even HoloLoens.
Native only gives you xbox