Yes, Dish and XB1 are compatible, however... at least in my case, I had to connect the console directly to the TV, walk the setup menus, have it recognize the TV, etc, then plugged in my Dish receiver (not the Hopper) into XB1 and after completing the setup,
everything started to work. Interestingly enough, after I first turned on the console and didn't see the XBOX home screen (I could watch TV just fine), I called DISH and they told me that my STB (EV722 is the model, I believe) was not compatible with XB1...
much to my surprise! Obviously, their tech support needs additional education, because I am sure I am not the only one who needed their assistance.
I don't have Hopper but I do have Dish and mine works with XB1 just fine. Plug your Dish reciever into the HDMI in port then plug HDMI out to your TV . Then go settings and go to TV & one guiide and it will walk you through the setup.