What does a plain reading of the Bible say about Homosexuality and how do we reconcile it with modern thinking?

We don't reconcile God's Word with modern thinking. Modern thinking, if it is to be valid, must reconcile with God's Word. Of course people don't choose their sexual orientation! Which is why sexual orientation is not a moral issue. But we do choose our behavior, which is why behavior is a moral issue. God has made it clear that sexual union outside of marriage is immoral. He has also defined what marriage is. Marriage between persons of the same sex is impossible by definition (look up the definition of "marriage" in the dictionary), a fact that no civil decree can change. Therefore homosexual acts are always immoral, as are heterosexual acts outside of marriage.