The reasons are similar to the arguments for homosexuality being potentially moral. (Note, while you may disagree, this is called "answering the question...")
Scriptural reasoning against the practice is, frankly, thin.
You have basically two lines of Biblical argument.
First, rules based - there's some mentions in Deuteronomy (22:5) that sound like all the "don't eat shrimp" kinds of Jewish law restrictions we don't use under the new covenant; plus there are plenty of Biblical figures that didn't align with gender standards of the times that don't get called out on it, while Jesus says "don't worry about clothes" several times during his ministry. Deuteronomy 23:1-2 seems to say "no eunuchs" but Jesus in Matt 19:12 and Acts 8:27 kinda put that on blast. I think it's fair to say that without going in with a presupposition, there's not a clear Biblical red line here. (Even among our Jewish brethren that do hold to the law there's more complex views about what it requires...)
Second, there's the more general "but, God made them male and female."
Genesis 1:27 So God created mankind in his own image, in the image of God he created them; male and female he created them.
And its reiteration in Matt 19:4.
Yes, but we live in a fallen world now. People are born in all kinds of intersex manner. The Bible isn't a science book, the sun doesn't go around the earth. The exact same chapter talks about "And God called the light Day, and the darkness he called Night: and the evening and the morning were the first day" but we don't refuse to recognize the other shades of daytime not enumerated there.
The LORD formed me in the womb (Psalm 139:13) but people get born with Down's syndrome and we take prenatal vitamins and some have birth defects we conduct operations to correct. This line of reasoning is a lot like "well woman was cursed to have pain in childbirth so painkillers aren't OK..." Sure, some fringe denominations believe that but it's not part of mainstream Christian thought.
If it's kind of unclear and mostly old-testamenty, what are we to do? Well, 1 Corinthians 8 and 10 give us some guidelines from the ol' eating meat sacrificed to idols question. My TL;DR - Some people think it's wrong, others don't, be convinced in your own conscience (but really, it's not, come on, God's bigger than that...) See also The Tyranny of the Weaker Brother.
Whereas Scriptural admonishments to love your neighbor, etc., are clear and compelling.
I'm Episcopalian, and we include LGBTQ+ folks including trans people, including for ordination (search "gender identity" in The Acts Of Convention for deets) and this is effectively the grounds for their and other denominations' stance of prioritizing love instead of exclusion. It's often just mentioned alongside general LGBTQ+ inclusion, see also Episcopal Church: Transgender Rights for Episcopal articles on the topic.
Same deal with, for example, the Presbyterian Church that I was a youth minister for back in the '90's. Many professional theologians better trained than your uncle on Facebook have evaluated it and come to the same conclusion, so it seems to me in the scope of mainstream Protestant Christian practice.
So TL;DR many Protestant church theologians say God's love and community
a) includes even sinners, duh and
b) it's not real clear this is a sin.
What's The Real Question Here?
Of course most people asking whether being transgender etc. is moral aren't asking because they are trans and really want to know if it's a sin. They want to know if they can be rude to, discriminate against, etc. those who are.
There is a super clear Biblical answer to this and the answer is no. An even basic canvas of the Gospels reiterates how Jesus eats with prostitutes and sinners. Lying, theft, and adultery are big 100% clear Christian no-nos, but you don't publicly attack those people. Catholics don't believe in divorce, but if someone's divorced and remarried, the Church may not recognize it, but they are still referred to as "Mr. and Mrs. Whatnot."
Every generation you can pick some Bible verses and use them to abuse those who are different - from actors and scientists in the more medieval times to women who work or have short hair, or black people who are uppity enough to not want to be slaves or have interracial marriages, or dance, or plan the devil rock and roll music with the gee-tar, or any number of similar things.
Matthew 7:4 How can you say to your brother, 'Let me take the speck out of your eye,' when all the time there is a plank in your own eye?
Seems to me there's plenty of murder, greed, lying, cheating, and so on to be up in arms about, things that are restated scores of times as being really actually bad, and past that maybe treat everyone polite and realize that you may think they dress funny or their food is weird or their car is too ostentatious or they date someone you don't like, but that's all down in the small details of being a loving Christian community. Because that's more important than whatever picky little point you want to make so bad.
That's the point of a lot of the other Episcopal etc. church rulings against discrimination, bathroom laws, and so on. Whether or not you believe it is moral to express a transgender identity, etc., you are responsible for having a Christian response to it yourself, and what that is is writ pretty large across the Bible.
Matthew 22:36-40 "Teacher, which is the greatest commandment in the Law?” Jesus replied: “'Love the Lord your God with all your heart and with all your soul and with with all your mind.’ This is the first and greatest commandment. And the second is like it: ‘Love your neighbor as yourself.’ All the Law and the Prophets hang on these two commandments.”