They're not asking for God's approval. Really, from a religious perspective, they're not asking to get married at all. They just want a separate and distinct legal agreement which the state happens to have (unfortunately) given the same name. Those of faith should know that the state has no power to grant legitimate marriages in the eyes of God anyway, right? You need a religious ceremony for that.
If I were a religious man, I wouldn't consider this legal union to actually be "marriage" at all, whether it's a man and a woman or two men or two women. If God doesn't recognize this union, it's not really marriage anyway, is it? So why insist that we hold it to a religious standard of one man+one woman?