So you would have believers and non-believers realizing what they believed in is wrong. I imagine the world would descend into chaos.
If proof of simulation existed, I think it would be more abstruse, e.g., error states in quantum field theory. If this proof were only accessible to the intelligencia, I doubt the reaction would be very different from that of a new religion. Some would proclaim divine providence like the prophets of yore (perhaps it was a miracle, or perhaps they just saw Jesus in the toast). I doubt anything short of an exploitable error would cause a disturbance to life as we know it. On the other hand, if we could exploit it...