I have a hard time seeing how using a scythe could be inherently ambidextrous. Other activities that involve swinging, such as with a baseball bat or golf club, are done in either a right- or left-handed fashion. Even when
splitting wood, when the swing is vertical, the maul is held in either a right- or left-handed grip (depending on which hand is on top).
Yes, scything involves swinging in two directions, but I've spent the bulk of my swinging-things life directing force in a particular direction (to the left, as a righty), and I can't imagine swinging a scythe blade the other direction without looking like a baffoon. If I were a lefty, I would certainly make a point of hunting down a left-handed scythe.