XNA is mature and not dead, which actually makes developing with it easier than if it were still growing. Just like in human relationships, mature is better !
Monogame is really the way to go, but either way, games made with XNA or Monogame will run for years in people's devices.
Enjoy the development environment for years to come, stop complaining, and start making money with games soon! Construction on the doorway has practically stopped, but the Door is still open!
This is a great answer that touches on one other important point: the fact that XNA is no longer being developed means that the API has stabilized. Means that you can safely develop using XNA now and know that your code is still going to run and be valid in 5 years time as Microsoft won't be pulling the carpet out from under you by changing the API.