Is it possible to be a crossbreed?

[Zojha]

Anything more "exotic" than this, however? No. There is, currently, no lore basis for it, and if you are trying to RP in the bounds of the established XIV lore, there's no example for it.

There is no examples, however...
http://forum.square-enix.com/ffxiv/t...l=1#post490835

Ferne has long since confirmed the races can inter-breed, without giving any restrictions to boot. How the offspring looks however is a different topic altogether.