What does Buddhism literature and tradition say about transgender folks?
The Bodhisattva Avalokitesvara can be seen as having an indeterminate gender. Quoting from this website 


  One interpretation of this development contends that the bodhisattva
  is neither male or female but has transcended sexual distinctions
  [...] the flowing drapery and soft contours of the body seen in
  statues and paintings have been intentionally combined with a visible
  moustache to emphasize the absence of sexual identity.


So the issue of gender can take on a more flexible interpretation with some more Mahayana aspects of Buddhism