The following is a video of Michael Coogan, editor of the New Oxford Annotated Bible, explaining the view on LGBT based on the Bible.
He explains how gender identity started off as somewhat fluid, since the first human had no gender, and then was split into Adam and Eve.
In the New Testament, Paul explained the concept of equality. He said that there is neither Jew nor Gentile, slave nor free, male nor female. This could be interpreted as Christians recognizing equality. Paul could be referring to the unity that we once had at the beginning of time, when Adam and Eve were created.
This is one of many interpretations of the Bible.