Part of the problem is understanding (or the lack thereof) why the church doesn't approve of gay marriage.
Is it because they hate gay people, and want them to suffer for their "choices"? That's a popular one, and it gives everyone who has an ax to grind a nice foothold, but I don't believe that it's the core of the issue. The church has stated that they don't oppose civil unions (or domestic partnerships) with all the same rights as a marriage. So why are they so hung up over a word?
IMO, it has less to do with the marriage itself, and more with the definitions of elements of LDS doctrine. Allow me to explain:
A major doctrinal cog is the Law of Chastity. This specifies that each person is to have no sexual relations outside the bounds of a legal and lawful marriage. They don't even have to be married within the church. Just legally recognized. Say you're homosexual and LDS (it happens). You and your partner get married, live every other facet of the mormon lifestyle, and go in and request a temple recommend from your bishop.
Here's the tricky part: At the letter of the law, you are obeying the LoC, right? But the church always has (and always will) considered homosexuality immoral and improper. Of course, the leadership is going to deny your request.
Bring on the litigation. So you see, there could be a bit of a slippery slope.