* They treated "gay" as an identity and a cohesive group, instead of treating the subject as human beings who engaged in particular acts, or had certain proclivities. The moment same-sex attraction and sexual activity was no longer about action and instead was about actual existence - the moment it was no longer about "sodomy" but "gay people" - they set themselves up to be easily portrayed as persecuting a helpless group, rather than disapproving of particular behavior.
* They succumbed to using the language of the people who opposed them, forgetting that language determines sound bites, and sound bites determines how a lot of people think. "Opposing gay rights" is like "opposing women's rights" - even if the right in question is abortion, it sounds bad, and it cements the idea that what they're opposing is, in fact, a right. It also feeds into point one, where again the focus is on the people and not the acts. This is one reason why the pro-life cause has actually had some success - they refused to be "anti-choice", and when the opposition talks about "reproductive rights", the pro-life side talks about "abortion" and "murder in the womb".
* Working off 2, they shied away from explaining what they were actually opposing, possibly because of worries about language - allowing the opposition to be the ones to define what they were opposing. Oppose "homosexuality", and you're painted as (once again) picking on a group of people for having urges they had no choice in having - and yet, that's exactly what Christians allowed themselves to be painted as. Why? Because they treat the actual topic - sex and sexual activity - as off-limits, whether due to politeness or embarrassment. Which, in turn, allows their opposition to state things in the most dressed up ways without complaint. LGBSA groups defend "the right for two people, of any gender, to love each other". They never defend "fucking someone in the ass as sacred and pure". This is, even now, rather tough to defend.
* Working off 3, they blanket-condemned homosexual relationships without pointing out that, if you remove the sexual aspects, there's little to anything left to condemn. This is probably the most controversial part for any traditionalist Christian (and I am one myself) to accept in this post, and is no doubt in need of more clarification than I care to give at this point. But I stand by it. Remove the sexual aspects from a 'gay couple', and what are you left with? Pretty much, very close friends.
There's more to this, but these are the key points which bug the piss out of me. The language in particular, and I grind my teeth whenever I see a conservative Christian saying he "opposes gay rights". I know what he's saying, but he doesn't understand how it sounds, and what effect that has on his argument.