Not long ago, that was the same argument used to justify banning interracial marriage. Not long before that, it was the same argument used to justify support for slavery.
And namely, it's not an argument. It's: "God told me this, now you must obey me. By the power of this holy book I'm waving around, I have the right to deny your rights."
Well. You don't have to recognize a gay marriage. The government can't compel you to think certain thoughts. However, your recognition, or lack thereof, is irrelevant. The government recognizes the marriage as valid, and the world will keep turning with or without you.