Is civil marriage between a man and woman more correct in god's eyes than a gay civil marriage? Neither will get you exaltation. Both are just a government recognition of a contract. They aren't temple marriages. So essentially you're saying you don't want to participate in a legal formality that's meaningful to the couple. That's fine, but don't pretend you're taking some kind of moral stance, or you personally have a mandate from god to condemn it. God probably doesn't care. He's probably more concerned with the actual sex act and other behavior keeping them from having a close relationship with him. Just like you have sinful behaviors that keep you from a full relationship with God.

Don't do something you're not comfortable doing, but wouldn't you change your opinion if your daughter or son decided to enter into a gay marriage? Would you be there? Would you participate? Maybe you wouldn't, but I wouldn't be able to, and that's where my head is when I say show love.

Side note: I don't believe the church will ever allow temple marriages of gays (it doesn't jive with the plan of salvation IMO), the prophets has been pretty clear on that.