The emotionally disturbed aspect to which you refer is perfectly, and charitably understandable.
If you truly believe in your heart of hearts that for some reason you cannot explain, that your external body does NOT match what you are convinced you truly are, it is an unimaginable burden. And many of these people are proving to have dissonance between their genetic makeup and their physiological make up. I suspect as science advances, we will learn of, and be able to quantify, more and more of these dissonances. Some within the homosexual community, as well.
Suicide, drug abuse, promiscuity stemming from self worth issues (like a rape victim) self mutilation, and depression are a plague for these people. And those are often the RESULT of, NOT the CAUSE of, being transgendered. They struggle for YEARS before they reach this conclusion. NO ONE simply wakes up one day and says, “I’ve got it! I’m transgendered!” (Or homosexual, or both.)
Understand that a transgendered person is required to “live” as the sex they will assume for a period of time before they are allowed to begin hormone therapy and plan for surgery. They usually prefer to be called by the gender with which they identify.
And unfortunately, doing otherwise, may expose them to great harm. As Christians, we must take responsibility for actions we take that harm others, whatever our intention may have been.
The statistics showing how many of these children of God are cut off from family and friends for acknowledging their identity is heart breaking. They often lose jobs, are forced to relocate and “start over” and change their names. They are at substantially higher risk for physical violence and harrassment than even homosexuals.
If you just don’t “get” transgendered people, that’s okay. Just thank God that you were given other crosses to bear. But love them anyway. Whether self assured, confused, confident, or just plain weird, they all have scars. So do you and I. They just may be internal rather than external.
Caveat: NO, I’m not transgendered. Or homosexual. But I’ve known a good many since childhood – they all say I was the only one “who didn’t judge, and just accepted them.” I don’t fully understand it all. I just know that my job is to love people, as best I can. Some days, through the grace of God, I get it right. Other days, the grace of God lifts me up when I get everything wrong.

But I try anyway.
Summer