Better known in the West as the Eastern Orthodox Church, the Orthodox Church is unique in that has not changed since the first few centuries of the Church except superficially (language, location, etc.). Orthodoxy is important to me personally because virtually all my own theology is Orthodox, I presently attend an Orthodox church, and I may do so the rest of my life.
Jesus' feminine qualities
The good news is that the Orthodox Church relies on Scripture and the Church Fathers for authority. The Orthodox divides up matters into Dogma and Speculation (theologumena), the latter containing matters that are not known directly through either authority. Any doctrine about transgenderism will always be speculation because Scripture and the Fathers (to my knowledge) do not address it explicitly.
The bad news is that Scripture, for its positivity, is not clear and the Fathers' occasional comments are negative. For instance, gay sexuality is criticized because males are taking the sexual position of females. Orthodoxy, like most of the Church, criticizes transgenderism for usurping God's supposedly ordained Creation dynamics. Unlike other denominations, Orthodoxy views little of the Bible as culturally relative; therefore, aspects like God's pronouns and gender roles are not culturally based but universal. It publishes Salvo magazine.
Transsexualism and Eastern Christian Thought - A site about being transgender and being Orthodox