Update:
I uninstalled rewired, uninstalled UFE2.5 Source, then reinstalled UFE2 Source, reinstalled rewired (the most recent updated version), followed the entire rewired steps for UFE2 in the document, and the results were the same. Except now Button1 is super sensitive in the Main Menu Screen. One press goes to the Versus Mode Screen and then immediately back to the Main Menu. When I get to the Character Select Screen, it still switches Player 1 Joystick to Player 2, the Player 2 Joystick no longer functions Screen and the buttons on either Joystick has no response. Which means that I am currently unable to go beyond the Character Select Screen.
Also there are no custom controls, all of the control layout (in rewired) are the default setting. The names for both players are still Button 1, Button 2, etc.
I am not sure if it's a UFE2.5 bug, or if Rewired was not optimized for version 2.5, or if I am just doing something completely wrong, but whatever it is I'd like to get this fixed.
Rewired was working perfectly in UFE2.4.1, but UFE2.5 rewired seems to be a lot worse than when I was having problems a few months back.
If you have any solutions, please let me know.