I suspect that this isn't going to have very much effect, since people opposing homosexuality are likely to do so out of a instinctive revulsion and rationalize the reasons afterwards. (Note that there are both religious and atheist homophobes, and both religious and atheist people who have no problem with it.)
Obviously it's not foolproof, but I've seen many cases of people almost automatically becoming more tolerant of homosexuality (and becoming more moral in general) after they lost their faith. (This blog post is one very well-stated example. Warmed my heart.) Admittedly, it can work the other way too: I personally know a few ex-Mormons who left the church after (and, certainly, at least partly due to) their becoming more accepting of homosexuality. But don't discount the first case. There may be some natural revulsion to homosexuality, but when one lives in a society that increasingly has a revulsion to that revulsion, maintaining it requires that one have something very emotionally significant for it to feed on. Religion and homophobia may not cause each other, but they have a mutualistic symbiotic relationship.
I'd like to see some studies on that, though. We could find people who were raised religious (or became religious) but later became non-religious, and ask them their positions on various social/moral issues before and after their deconversion. In instances where their views changed, we could ask whether (in their estimation) it was more of a cause or more an effect of their deconversion.
I recently told a friend that I was planning to write (and post online) a paper that rigorously refutes every argument1 I’ve ever heard that homosexuality is inherently immoral. The purpose of this effort was to provide a handy link for people who want to persuade family members or friends who are marginal believers of the homosexuality-is-immoral theory. As a key part of this effort, I intended to demonstrate that the predominant religious arguments against homosexuality cause contradictions within the religion. For example, the tortured reasoning of the Roman Catholic Church2 goes like this:
This argument seems to be logically valid, if you accept the insane assumptions. Bizarrely, though, the Catholic Church also recommends a practice called "Natural Family Planning", in which married couples who want to prevent pregnancy have sex only when the woman is believed to be infertile! To be consistent, the Catholic Church would have to oppose such deliberate efforts to prevent natural reproduction.
My paper was going to be full of little examples like this, of how opposing homosexuality leads to contradictions within Christian Virtue Ethics, established interpretations of the Koran, or whatever. However, my friend told me that he thought my efforts were misguided. Why try curing these folks of the splinter of intolerance, when they still have the wooden beam3 of theism in their eyes?
After all, if someone you know is planning to quit her job and move to Alaska because her horoscope told her that Tauruses need more spontaneity, you shouldn't tell her to stay because she's actually an Aries. You tell her to stay because astrology is provably bogus.
I'm uncertain. Most of those wooden beams are staying right where they are for the foreseeable future. But attitudes toward homosexuality are changing relatively quickly. On the other hand, there is something to be said for striking at the root of the problem. Overall, I'm leaning toward making these smaller arguments instead of trying to convert people to atheism.
**A lot of people have said they don't think this approach will be very effective. I mentioned in the beginning of the article that the purpose was to help others persuade marginal believers of the homosexuality-is-immoral theory.
1. Most of these arguments are religion-based.
2. Ironically, the Catholic Church is an easier target because they have the decency to actually lay their arguments out formally (though often in gratuitous Latin), since they believe that the Church's dogma can always be confirmed using pure Reason. Protestant churches tend to simply cite scripture--and they believe the scripture because they have faith. Yes this is a tautology. Actually, I wonder if the Protestants' refusal to justify their beliefs rationally protects them from Escher-brain effect. Faith claims can be neatly compartmentalized, sequestered away, protecting the rest of the mind.
3. A reference to Matthew 7:3.