From berdache +‎ -ism.

berdachism (uncountable)

1. (anthropology, now offensive) The state or practice of being transgender or third gender in a Native American society.
   • 2000, John W. M. Hallock, The American Byron, page 19:

     English settlers, in turn, solidly repressed berdachism in North America, although a score of nineteenth-century texts reveal a lack of sexual assimilation.

• See usage notes at berdache.

• two-spirit