I watched the Evancho fanily special and I must admit that I was not too comfortable with the son changing from a boy to a girl. However, to be fair, I think that we should all ask ourselves, what would we do if we had a son or daughter who felt extremely strong about this matter and acted like a member of the other sex from the time they were very young, say age 4 or 5? Would we tell them that we would disown them or would we support them and love them no matter their decision? Yes, we might tell them that God might not approve of such, but to say that a sex change means that someone is headed for Hell is a bit much, in my view. Only God can make that decision and nothing in Scripture specifically forbids a sex change. It is not the same as homosexuality. Truth be told, it is a messy subject and most of those who undergo the change probably endure many years of psychological hardship.
First, no, I wouldn't disown a child of mine for that (or pretty much any other) reason.
Now that's out of the way...the reason why I don't have a problem with gays but trans seems "kooky" to me is that I can at least understand a gay person. I love my wife, he loves his partner. It's the same feeling, albeit directed differently. Quote me all the bible passages ya want - they may or may not apply. But on a conceptual level, sin or not, I at least can grasp what they're going through.
Also, every gay person I've ever known simply wanted to be left alone and not proselytized to. I know there's all this malarkey out there about "the gay agenda" - but the "gay agenda" basically boils down to "hey, don't give me crap for being gay, let me have the same legal rights you have, and don't try to levy the state against me". That's pretty much it in a nutshell. Evangelicals may whine about how their "freedom of speech" has been curtailed - but that really boils down to "my freedom to be a jerk to you over your lifestyle and tell you how you're damned". If those are their goals - and so far as I can tell they are - I have no beef with them.
Trans - I don't feel the same way. I don't understand trans. I can't grasp their experience. Why? Because I give ZERO thought to my sex. And by zero, I mean absolutely zero. If someone were to ask me "What's it like being a guy?" I would tell them I have no clue. I don't know what it's like to be anything other than myself. I don't know if how I experience the world is more similar to how some other dude experiences the world on a basic level than a woman. Sure - we may have different things HAPPEN to us as a consequence of our sex - but that's different than what it feels like to actually experience things.
My belief has always been that while circumstances may differ, the way things actually feel as a man or a woman aren't likely all that different. Like if you were to switch me into my wife's body for a few days, I don't think there would be any profound "Hey, this is what being a woman feels like, and it's SOOO much different."
So to that end - I don't even understand where someone is coming from when they say "I feel like something I'm not" What does that even mean? And since you have no basis for comparison between the two, how do you judge that?
To me it seems like a mental illness. I wouldn't ostracize a family member for being schizophrenic. I wouldn't deride them for it. I would try to work with it as best I could. Same thing with being trans. But it doesn't mean that I think it's sane, or that I'm going to suddenly innately BELIEVE that there are all these different genders walking around.