Ah, but it does. Its prophets have been deceived by Satan regarding hatred and oppression of gays, just as they were in recent eras regarding the "accursedness" of black people and the acceptance of the immoral polygamy culture (which might have been okay had it been just people's free choices of whom to love, but unfortunately also involved coercion, statutory rape, and the deliberate impoverishment of male children to eliminate competition for the teenage girls).
You can look at other occasions where people who believed themselves moral leaders at the time can now be clearly seen, in retrospect, to have been on Satan's side, whipping up hatred and intolerance in God's name taken in vain. The Crusaders, the Inquisitions, the Old World anti-semites, the righteous pro-slavery preachers in the time of the abolitionists, the segregationists in the civil rights era.
The devil's tricky, though, right? As Matthew 4 tells it, he even tried to tempt Jesus into accepting rulership over the entire world. (Interesting how LDS doctrine one-ups that temptation and offers, to the highest elite, rulership over their own entire universe. Very interesting.) There's always scripture that seems to support whatever temptation to hatred and persecution (infidels, heretics, Jews, slaves, blacks... or gays) Satan is pulling out of his bag of tricks this year. It can get very confusing.
So here's a solution that has always worked. Ask yourself, which side is doing harm? Are gays doing harm by loving one another and marrying one another, or is the harm coming from the people trying to prevent that?
And, very importantly, the harm in question can't be vague invisible spiritual harm. That doesn't count. It didn't count for Jesus; he said so in the parable of the Good Samaritan. Samaritans at the time were a variant sect of Judaism, with slightly different beliefs than those of the Jews Jesus was preaching to. Accordingly, the "mainstream" Jews regarded the Samaritans as worthy of contempt because of all the spiritual harm they were supposedly doing by practicing different beliefs. Jesus's teaching was to disregard all that; the Samaritan in the fable was doing good in the world in the present and that was, and is, what counts. Those who would bloody their neighbor's nose out of concern for his soul are doing wrong. The state of his soul is up to God, and way beyond the reach of your fists or your bigotry.
Satan is very big on this idea of invisible spiritual harm. It's one of his best tricks. It can lead even a prophet into claiming nonsense like "male and female are eternal" when the Bible clearly says that there is no male or female in heaven, and no husbands and wives in the kingdom of Christ. Old Scratch laughs and laughs at the real-world harm (such as, lifelong partners denied one another's company when one of them is ill or dying in a hospital, or simply the spectacle of intolerance and violence of neighbor against neighbor provoked by the supposed prophets of a loving and forgiving God) that his simple trick invariably leads to when used on the wrathful, the pridefully pious, the uncharitable.
That is how the Church of Jesus Christ of Latter-day Saints (and, to be fair, many other churches) support evil and immorality, even though they and their members often did not intend to. It's a good thing for you that God is loving and forgiving.
Respectfully,
Myriad
). Unless society itself changes, I predict gay marriages in the temple within another 50 years.