With Homosexuality, I get the basic logic behind saying "God made genders for a reason", it's not Biblical so I reject it, but I get it.
I don't get this notion that claiming you were assigned the wrong gender somehow insults God. Not if coming from a fellow Six Day Young Earth Creationist. But that one Calvinist blog has been obsessing over Caitlyn (who they insist on calling Bruce) Jenner lately. Endorsing outdated secular evolutionary psychology.
Saying "God didn't create you the wrong gender" is to me a horrible lack of Biblical literacy. God only directly created two human beings. Adam, and Havvah/Eve who he cloned from a sample of Adam's DNA. They were ordered to reproduce before The Fall, but it seems they did not succeed in conceiving any offspring until after it.
All of us are merely imperfect copies of Adam, all to some degree corrupted by The Fall, but many with more blatant errors then others.
People are born Blind (John 9), Born Deaf and Mute, born with physical and mental handicaps, born with extra-limps and lacking limbs, born conjoined, born with all kinds of mutilations and deformities like The Elephant Man.
Because of The Fall no Creationists consider any of that evidence against intelligent design. But some have trouble with the Idea of Sex and Gender getting messed up? Genetically it's mostly a matter of how the chromosomes interact, really a fall simpler thing to become screwed up then what causes all the above.
Transgender people aren't labeled Intersex, because there seems to be no physical different between them a Cis person assigned the same gender they were assigned based on merely studying the anatomy or even DNA (Though we actually understand less then 10% of the Genetic code).
However many brain scans of Transgender people have shown that their Brains do operate like the gender they identify with, not the gender they were assigned.
Being Transgender is an issue The Bible doesn't directly address unless you see it in some way relevant to the crypt statement about being Born Eunuchs.
To all these people think gender should be determined by physical anatomy only and has nothing to do with the mind, soul or spirit of a person, while also agreeing with Genesis 1 that God made only two genders. How do you determined the gender of intersex people? particularly those who fully have both sets of genitalia?
We have people who want to make verses about Cross dressing relevant. Even if such verses did condemn any and all gender divergent dress, transgender people are by definition irrelevant to those verses if their claims are true. Or if anything they may feel (if Bible believers) like they're violating them when they dress as their assigned gender.
But we are not under The Law, and those commands were there to condemn specific Canaanite ritual prostitution related pagan practices. This idea among some legalists that they condemn women wearing pants is frankly absurd. Just as absurd as the Rabinics who think "don't boil a kid in it's mother's milk" refers to Cheeseburgers.
My personal belief that the Holy Spirit has lead me to, is that Transgender people who are saved will be in The Resurrection the gender they identify as, not the gender they were assigned.
And as Paul made clear in Galatians, in the Church there is neither Male or Female just as there is neither Jew or Gentile.
Update: Here is a website trying to deal with Trans issues from a Rabbinic Jewish perspective. It's an interesting read. But not entirely in agreement with my views. Since I'm not Rabbinic, and since I consider a Trans person the gender they identify with even before transition.