Which sport are you not allowed to play left handed?

POLO !

Polo must be played right-handed. Left-handed play was ruled out in 1975 for safety reasons. To date, only 3 players on the world circuit are left-handed.

https://en.wikipedia.org/wiki/Polo

Polo

https://en.wikipedia.org/wiki/Polo#Players

According to http://www.anythingleft-handed.co.uk/lefty_disadvantages.html it is also Hockey

These NHL players were all left handed.

Sport - Hockey
Name Nationality Description DOB

Barrasso, Tom USA (Mas) Hockey Player 31-Mar-1965
Cashman, Wayne Canadian Hockey player - Boston Bruins 24-Jun-1945
Esposito, Phil Canadian Hockey Player
Bennington, Holt USA Ice Hockey player
Fuhr, Grant Canadian Ice Hockey player
Kurri, Jari Finland Ice Hockey player 18-May-1960
Neely, Cam Canadian Ice Hockey player
Orr, Bobby Canadian Ice Hockey player
Sawchuk, Terry (Dec'd) Ice Hockey player
Turek, Roman Czech Ice Hockey player

http://www.anythingleft-handed.co.uk/fam_sport.html

When I played field hockey at school (back in the 60s), all hockey sticks were made with the same side flat, so all players had to use the same grip and stroke. A real disadvantage for us lefties! As far as I can find, this is still the case, although there is nothing in writing forbidding having the opposite face flat and playing left-handed - the only stipulation is that only the flat face can be used to strike the ball.

"The stick in England, possibly because of the close association with it of cricket players, developed with a stick with just one flat playing side, the left face, below a round grip area - with the use of the right-face side, which is rounded, prohibited - an oddity that had a profound effect on the later development of the hockey stick and of the game itself."

https://en.wikipedia.org/wiki/Field_hockey_stick