If you google up a survey of conservative Christian condemnations of transgenderism or gender fluidity, you'll notice that they pretty much all go back to the creation story in Genesis 1:
So God created mankind in his own image, in the image of God he created them; male and female he created them.
That's the approach, for example, of the Focus on the Family article "A Biblical Perspective on Transgender Identity".
Those of us committed to the Christian worldview base our view of gender and sex on the biblical book of Genesis
The Christian Q&A site "Got Questions" gets a little more precise: It admits the Bible doesn't cover nonbinary gender issues specifically, but invokes Genesis as the best it can do:
The Bible nowhere explicitly mentions transgenderism or describes anyone as having transgender feelings. However, the Bible has plenty to say about human sexuality. Most basic to our understanding of gender is that God created two (and only two) genders: "male and female He created them" (Genesis 1:27). All the modern-day speculation about numerous genders or gender fluidity—or even a gender “continuum” with unlimited genders—is foreign to the Bible.
Both articles (and all the others I've found claiming that the Bible mandates exactly two genders) share an interpretative choice: "male and female" is read as prescriptive, not expansive. Male and female, in other words, aren't examples of the breadth of God's creation, they define the limits of it. That's the choice Got Questions is making when it says "and only two". Once you make that choice, you can claim that anyone talking about some possibility outside the male/female duality is going against God.
Here's my brief observation: That's a weird interpretation.
In particular, that's not how anybody reads similar poetic forms in the rest of the creation story, or in the Bible in general. In Genesis 1:11, for example, we read:
Then God said, “Let the land produce vegetation: seed-bearing plants and trees on the land that bear fruit with seed in it, according to their various kinds.”
While 1:24 says:
And God said, “Let the land produce living creatures according to their kinds: the livestock, the creatures that move along the ground, and the wild animals, each according to its kind.”
Think about those. After God says "vegetation", does God then intend to legislate that plants must produce seeds? Mosses don't. Neither do ferns; they rely instead on a complicated two-generation reproductive cycle that involves spores. Are they in violation of the divine command? For that matter, were human agronomists subverting God when they produced seedless watermelons?
What if an animal species fell somewhere between the categories of "livestock" and "wild"? (Cats, for example.) Would they be abominations? What about animals that move primarily through the trees rather than "along the ground"?
Now back up and take a wider view: Isn't the whole creation story an elaboration of the idea that God created everything? But the list in Genesis 1 doesn't include mushrooms or insects. Should we then assume they are unholy creatures that come from somewhere else?
Of course not.
In every phrase but "male and female", we read Genesis 1 as expansive and celebratory. The point is to stretch our imaginations by suggesting the breadth of creation, not to restrict creation down to the entries on a list.
"Male and female he created them" should be read the same way.