My sense is that many people with knowledge of Mormon theology believe that there is no way to reconcile it with gay marriage; that there is no way the LDS church could ever accept gay marriage. I disagree. I think it can be reconciled, and I don't think the church has to give up anything essential to do so.
Mormonism faces two main theological obstacles that prevent it from accepting gay marriage. These are its teachings about the nature of homosexuality and its teachings about the natures of men, women, and marriage.
First, like many conservative religions, the LDS church teaches that gay sex is deviant and sinful. Yet, even this position represents an evolution towards acceptance.
Formerly, the church taught that even the desire for gay sex is deviant and sinful. In other words, the mere fact that someone was gay made them deviant and sinful. Moreover, if the deviant sinner would just try hard enough, the church taught, they could become normal, i.e., heterosexual.
That is no longer what the church teaches.* Instead, it has haltingly moved towards accepting the reality that sexual orientation is not a choice for most people, that gay people generally cannot stop being gay no matter how hard they try. It now takes the view that gay people are tragically afflicted with desires that make them want to have deviant and sinful gay sex. In other words, the task the church assigns to gay Mormons is no longer "stop being gay," it is "abstain from gay sex."
Of course, the church is still promoting the homophobic and offensive ideas that gay sex and relationships are intrinsically inferior to heterosexual sex and relationships, and that gay people are broken and pitiable. Still, even that actually represents significant progress compared to where the church was, say, 20 or 30 years ago.
But the important point is that the church is already demonstrating that its doctrines on the nature of homosexuality can evolve. The church's teachings about ongoing revelation and the possibility of errors in the Bible mean that its doctrines can be quite fluid at times (though change is rarely if ever fast). The church has a way to substantively change its teachings while still being consistent with itself. It can say, as Bruce R. McConkie did regarding former teachings about black people and the Mormon priesthood, "We spoke with a limited understanding and without the light and knowledge that now has come into the world."
The church could begin teaching that gay sex is no different from heterosexual sex. (It could begin teaching the truth about homosexuality, in other words.) If gay marriage exists, the church could easily hold onto its conservative belief that that premarital and extramarital sex are sinful. It would merely need to address sexual conduct, and stop making a distinction between heterosexual and homosexual conduct.
That's the "easy" part.
The supposedly harder part, of course, is the church's teachings about the nature of men, women, and marriage. The church teaches that those who marry in a Mormon temple and follow the church's teachings to the end of their lives will remain married for eternity. Moreover, it teaches** that such married people will one day become gods and create their own worlds (or universes or whatever), which they will populate with their own spirit children, just as this world was populated with our god's spirit children (i.e., us).
So this is the core theological idea underpinning the notion of the inferiority of gay sex and relationships. They are inferior because they can never lead to the highest possible destiny for human beings, i.e., becoming heavenly parents who create spirit children who go on to repeat the same cycle with a new world.
But does Mormon theology necessarily require that to be the case?
There is no definitive doctrine on the mechanics of how spirit children are created. It's supposed to require one male and one female god, but the idea that it requires actual copulation and some sort of "pregnancy" no longer has a great deal of currency in the church, if it ever did.
In any event, gay couples are quite able to have children right here on Earth. Why couldn't they do it in the Celestial Kingdom? Are the beings there less capable than us ordinary humans? Are they less altruistic, less willing to provide whatever assistance is needed? Neither description would seem to apply to omnipotent, omnibenevolent gods.
So, unless coitus is the only possible way to create spirit children, I don't see any genuine Mormon theological obstacle to gay marriage. The church could teach that, just like heterosexual couples, gay couples can marry in Mormon temples and can advance some day as couples to the highest level of the Celestial Kingdom, where they will create worlds and spirit children to inhabit them. Perhaps they would require some sort of assistance from their fellows; perhaps not. They would be gods after all.
The teaching now is that those who marry in a Mormon temple and follow the church's teachings to the end of their lives will remain married for eternity. Moreover, such married people will one day become gods and create their own worlds, which they will populate with their own spirit children, just as this world was populated with our god's spirit children. That wouldn't change. Only the teaching regarding who can be married in the temple would change. There would be a large social change, but no doctrinal change would be required.
*Of course, there are still Mormons (such as Boyd K. Packer) who believe and teach the old ideas. But after Packer deviated from the de facto policy while his giving "talk," his worst rhetorical flourishes were tossed down the memory hole in the official written version. For that to happen to the second-highest official in the LDS church suggests that there is a degree of commitment to moving away from the old views.
**The church may have deemphasized the teaching of this doctrine -- Gordon B. Hinckley seemed almost embarrassed by it sometimes -- but surely it still forms a core part of Mormon theology.
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