I'm surprised by the number of nay-sayers here.
Obviously convincing someone of Atheism is better than convincing them of the acceptability of homosexuality, but that doesn't mean that the latter is bad. The comparison to swaying an Astrology believer (saying they're an Aries, not a Taurus) is not apt; OP's idea is not to trick them using theist arguments, but to point out the intellectual bankruptcy of believing both in tenets A and B. As a few of the others here have pointed out, the way to remove the wooden beam might be by removing it sliver by sliver.
I think a site such as this would offer an excellent resource for Atheists/Agnostics who regularly argue with Christians over this topic; during my own deconversion process, I was greatly aided by the likes of Professor Richard Carrier who did the scholarly work and laid out the arguments for me - it saved me months of time spent researching, reading, and seeking out sources.
One argument, OP, that I hope you address - I heard this from a bartender the other day. "I'm against gay marriage/adoption because a child needs influences from both sexes." A trite, easy to understand response to this would be wonderful (I'm sure everyone here knows the answer, but I'm trusting that knb will be able to write it with eloquent rhetoric).
"Should we take children away from single mothers, then?"
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.