There's a scene The West Wing where President Bartlet tears a strip off an evangelical Christian talk radio host. In the scene (you can see it on YouTube, or read a transcript), the evangelical tells Bartlett that the Bible says homosexuality is an abomination. Bartlet then launches into a series of rhetorical questions, asking how he should carry out other Old Testament rules which we'd now find ridiculous, if not downright evil: "My chief of staff, Leo McGarry, insists on working on the Sabbath. Exodus 35:2 clearly says he should be put to death. Am I morally obligated to kill him myself or is it okay to call the police?"
Let's call this the Barlet gambit: the President's argument seems to be that it's inconsistent for evangelicals to say "homosexuality is wrong because the Bible says so", because they're not also keeping these other rules which are also found in the Bible. The gambit is a favourite with people who argue with evangelicals about homosexuality: sometimes they even quote Bartlet.
Unfortunately, the Bartlet gambit fails as an argument.
What's wrong with it
Evangelical Christians have reasons why they're not keeping the Old Testament laws despite regarding the Old Testament as scripture. The question comes up in the New Testament itself, once we reach the Acts of the Apostles, where we read of the first non-Jews converting to Christianity (up to that point in the story, what will later become Christianity is still a movement within Judaism, although a few Gentiles are impressed with Jesus in the gospels). The Council of Jerusalem ruled that Gentile Christians are allowed to eat shrimp and wear mixed fibres and, luckily for penis owners, don't have to be circumcised.
So, according to Acts (which, like the rest of the Bible, is inerrant, remember), Christians sorted this stuff out in the first century AD. They aren't going to worry about atheists calling them hypocrites for wearing cotton/polyester blend while "hating the sin and loving the sinner".
Perhaps Barlet is specifically objecting to the evangelical's use of Leviticus, which does put homosexuality on a par with things which aren't kosher, rather than with things which are morally evil. Alas, even without Leviticus, there are other Bible passages which can be pressed into service against the gay, and you can rely on evangelicals to know most of them, because the issue has become a defining feature of evangelicalism. We could argue that these passages don't apply to modern committed homosexual partnerships, but evangelicals don't find these arguments impressive.
What to do instead
In the UK, many rank-and-file evangelicals are educated professionals. They didn't get into religion to give gays a hard time, and, unless they've completely disappeared up their own sub-culture, they tend to be a bit embarrassed by the anti-gay stuff. Still, because it's "what the Bible says", they feel they're obliged to go along with it anyway, even if the Guardian wouldn't approve (the evangelical jargon phrase for that sort of thing is that it's a "hard teaching" where you'll just have to "trust God").
If I were a gifted orator like Barlet, I think I'd appeal to their sense of justice. Is there perhaps something odd about the way churches accept straight couples who are openly in their second or later marriage (something about which Jesus had some strong words to say), but wouldn't be happy with an openly gay couple? Some hypocrisy there, maybe?
Or we might try empathy. There's the problem that, as Valerie Tarico says, evangelicalism "can re-direct our mother-bear instincts away from protecting vulnerable individuals and toward protecting the ideology itself. Believers may come to feel more protective of their religion than they are of actual human beings." Still, it might be worth a go: is it fair to say that gay people cannot form committed romantic relationships? Imagine yourself in their shoes. If you obey the evangelical rules, it seems rather a lonely place.