Polo, field hockey and jai alai are three sports that specifically ban playing left handed. Polo and field hockey ban left handed play for safety issues, while it is impractical to play jai alai left handed.
In Polo, holding the stick in your left hand to pick up the ball necessitates approaching the ball at high speed from the opposite direction as a right handed player and would increase the rate of injury.
Field hockey does not allow left handed hockey sticks because the tackling a left handed player from a right handed players perspective would cause a higher rate of injury.
Jai alai players must wear the cesta, the wicker basket used to throw and carry the ball, on their right hand because there isn't a wall on the right side. Wearing the cesta on your left hand would make the game extremely difficult to play.