I tried binding it to a keyboard key, but it still caused the game to reset when pressed. I’ll try simply not binding it to anything as well, but frankly I’m not expecting much, it seems like RetroArch is dead-set on R3 being the MAME reset button.
UPDATE: Yes, Virginia, there is a Santa Claus.
Not mapping R3 did the trick. Thanks dude, you’ve been most helpful! 
ONE LAST UPDATE: Then I accidentally hit the L3 button too.
So now I’ve unmapped them both.
It helps that I’ve never played a game where striking the thumb buttons under the analog sticks was necessary.