"The Bible’s core belief, the one that underpins Western culture, is that there are two sexes..."
Um, no. The Bible's core belief is that the world was created ex nihilo by a transcendent God, that humanity was the pinnacle of that creation, but fell from the glory for which were intended (image and likeness of God), and that the transcendent God first by giving commandments to a particular people (the Jews) and then uniting Himself to our nature in the person of Jesus Christ, sought and made possible our restoration.
That there are two sexes is an empirical observation about God's creation that is mentioned in Scripture, and which is important because it reflects his will in creation. It is not the Bible's core belief.