This is happening to me using 2018.2.14f1. It doesn't do this in editor, but in VS and then further in Xbox One my game is unplayable while two controllers are connected. When only one controller connected this works fine, no problems. The second I connect a second controller, all input fires multiple times in one press, like it is triggering on the "press" and then repeating like crazy.

Workaround:

Add a check to ensure a small delay between handling button clicks in the UI. When a button click is detected, check that it has been at least ~0.2 seconds since a button click was handled, otherwise do not action the button click.

Since the issue mainly affects buttons that navigate between scenes, this delay will not affect responsiveness, but does eliminate the problem.