The beginning would be for Christians to acknowledge the mountain of evidence attesting to the normalcy of homosexuality. They could try opening themselves up to avenues of thought that don't involve appealing to baseless "deific" condemnation. They could consider the fact that virtually every psychological authority on the face of the planet have been telling us for the better part of 4 decades, and in no uncertain terms, that homosexual orientation is normal, natural, healthy and not in the least bit a mental illness.
Then again, if scripture is the only thing they recognize as worthy of their attention, they should consider the fact that the Bible doesn't say nearly as much about loving, committed monogamous same sex relationships.
The passages in Leviticus (18:22 and 20:13), understood IN THE CONTEXT of the time and place, are not an admonishment against loving sexual relationships between people of the same sex but instead against sex as a form of domination and control. Besides, these passages are part of the Holiness Code which is not binding to modern day Christians (or anyone else for that matter).
The story of Sodom and Gomorrah was a warning against rape, inhospitality and xenophobia. The reason for Sodom's destruction is made clear in Ezekiel 16:48-50: pride, laziness, being inhospitable, neglecting the needs of the poor, greed, and idolatry (the worshiping of idols). Nothing about homosexuality is mentioned. If Jude 1:7 describes anything about the sexual immorality and perversion in Sodom and Gomorrah, it's describing RAPE.
1 Corinthians 6:9 was a mistranslation of the word "malakee". It's used elsewhere in the Bible to mean someone who lacks discipline or one who is morally weak, and never is it used in reference to sexuality or gender.
1 Timothy 1:9-10? Also a mistranslation. 1 Timothy was an admonishment against male prostitution, not committed, loving same sex relationships.
The words "physin" and "paraphysin" in Romans 1:26-27 have also been mistranslated. Contrary to popular belief, the word "paraphysin" does not mean "to go against the laws of nature", but rather implies action which is uncharacteristic for that particular person. An example of the word "paraphysin" is used in Romans 11:24, where God acts in an uncharacteristic (paraphysin) way to accept the Gentiles. When the scripture is understood correctly, it implies that it would be unnatural for heterosexuals to live as homosexuals and for homosexuals to live as heterosexuals.
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Short of demonstrating the meaning of the scripture, I suppose we could assign each Christian a gay buddy for a month to show them that gay people are just people. I'm not saying we force Christians to hang around for gay sex or anything, but to see just how "unscary" gay people are (sorry for using a made-up word).