Since I've been where you are when it comes to the religious belief v. the equal rights issue, I'm just going to tell you my thought process. May work for you, may not, but it's how I came to the reconciliation between the two that you seem to be looking for.
One man, one woman may well be the only type of marriage that God approves of. Like so many other things that God "thinks" or does, I just don't know, I can't always know, and even if I do know, even if the answers are revealed to me through grace, I might not understand why. That, to me, is the essence of being a Christian - not knowing the unknowable, but having the faith that everything that God does, whether we like it or not, is right for some reason, even if we don't understand the reason, the method, or the outcome.
But for me, the pull of equality could no longer be ignored or pushed aside, because I don't believe that God wants homosexuals, whom he loves every bit as much as heterosexuals, to be denied the basic right of protecting the one person they love most in the world. I readily confess that I don't understand homosexuality, I don't understand how I could feel the same love and attraction for another woman that I do for my husband. But I don't *have* to understand it for it to exist in others.
And since I don't know for certain God's reasons, then who am I to question them? Who am I to say "Yo God, you made a mistake with these people, but don't worry, we'll fix it down here"? Who am I to tell them that God doesn't want them to "do that", when I believe that He is the one that created them as homosexuals?
The conclusion that I finally came to is that I don't have the right to make that decision. I don't have the right to deny such basic equality to people. Whether I consider a gay marriage to truly be a marriage, which to be perfectly honest is still something I sometimes struggle with, is irrelevent. It isn't up to me to impose my idea of marriage onto others, it isn't up to me decide if it's right or wrong. Free will is a gift from God, and IMO, denying that gift of free will by denying the right of homosexuals to marry is a sin in and of itself.