To start off: I don't have an Xbox 360 gamepad. I have a Logitech Gamepad F310.
In former Monogame versions, everything seemed to work fine (except the trigger values, they seemed like they might be bugged, but I never did more than a minor test with them). I even have a finished game that I just tested to see if the gamepad was still working fine.
With the latest Monogame version, the D Pad doesn't respond. (There is a button switch on the controller that lets you swap the D Pad and left thumbstick input; D Pad does send a signal because it is successfully detected as the left thumbstick when that switch is on).
All of the other buttons work (except the boolean for the trigger buttons isn't working, but I have no way of knowing if they ever did for this gamepad). But for the thumbstick booleans (I didn't test the float values), they're inverted vertically. XThumbstickUp is detected when I'm pressing down, and vice versa.
Is it possible that we'll see this fixed in the future? I should really upgrade to a Microsoft gamepad anyway, but for people who play Monogame stuff with these controllers, it's gonna be really inconvenient.