I think you are oversimplifying things a bit. A person may find themselves experiencing homosexual desire without choosing to do so, agreed. But beyond the desire itself, the entire gay lifestyle, like any lifestyle, is composed of countless choices and acts of the will. Perhaps a man experiencing these attractions will decide they are not good and will choose to remain celibate, as a large number of religious people with same-sex attraction do. I know a man who does this very thing. Or perhaps a man will decide that these attractions are morally neutral and that he can indulge in them and chooses to do so. He seeks a partner, a choice. He decides to present more feminine, a choice. And so on. These are all choices. We are not our sexual appetites. My sexual desire isn't what I "just [am]." It's merely one small aspect of who I am.
On the other hand, is my being a Christian "purely a choice," as you say? No, I don't think so. I can choose to eat pizza instead of ice cream, but I can not choose to stop believing that Jesus is the son of God. Can you choose to stop believing that the world is round? Our beliefs don't work like that. Of course as a Christian I do engage in countless choices and acts of the will on my faith journey. I go to mass, a choice. I receive the Eucharist, read the scriptures and so on, all choices. But really, my faith is not a choice for me. I feel I cannot do other than to believe and because I believe I see this as a gift from God, that I did not earn.
I do think there are actions we can take that will help us to change our beliefs, but I don't have time to ramble on now. I'm at work...