I don't think the OP is oblivious to this motive. I think he just is accurately pointing out that they are objectively wrong and that intolerant fundies are far more correct than their critics regarding what the Bible says and was intended to mean. He is also correct that such motives are short-sighted, self-centered, and unethical. Because the Bible was designed to promote unreason and authoritarian intolerance, any efforts to give it a modern glow around the edges only empowers that core message and prolongs its undue impact on a society that would be better off and more moral if the Bible were disregarded as irrelevant to ethics or fact.
I also don't think his message will fall on deaf ears. Most of those LGBTs seeking to retain a Christian identity are not true believers. They are of the sort of shallow "I just want the label" Christians who are most likely to listen to reason and give up religion entirely. Also, there are non-believers among those arguing with Christians about Jesus' views on gays. They view it as a political/social strategy to rob the anti-gay bigots of their sole justification. It is a short sighted strategy that does long term harm and it won't really work anyway because, unlike on most matters of fact, Fundies are largely correct in their claims about what the Bible intended to mean, both morally and on factual issues.
And I dispute that those who choose to ignore Biblical condemnation of homosexuality, either because it refers to them personally or just because they think there's nothing wrong with it, are somehow
less true believers than those who choose not to cherrypick it out of their belief system. You can be against slavery and still call yourself a true Christian. You can be in favour of equal rights for women and still call yourself a true Christian. You can think that committing genocide is a poor way to solve your problems and still be a true Christian. You can meet psychics and magicians and not kill them and yet still be a true Christian. You can send your kids to bed without supper instead of stoning them to death when they talk back to you and still be a true Christian. You can think the universe is billions of years old and evolution an established fact and still be a true Christian.
Every Christian, no matter how fundie, ignores whole swaths of the Bible that they find inconvenient or wrong and this doesn't make them less of a true believer as a result. Someone who thinks that one can be a Christian without caring either way about a person's sexuality isn't fundamentallly different than someone who thinks that one can be a Christian without caring either way about whether or not the woman you're talking to is menstruating.
While I agree with you that it would be great if they'd just dump the religion entirely, the LGBT Christians
don't have that motivation. It's not what they're going for, so doing that would move them away from their desired goal instead of towards it. They like being Christians and they want their Christian faith to embrace them. They're not looking to abandon it over disagreement about one point.