Um, no, actually, it isn't irrelevant.

Marriage is not between one man and one woman because the Church says so.  The Church teaches that marriage is between one man and one woman, because, marriage, by definition, by it's very nature, is a commitment between one man and one woman.  The Church teaches what manifestly IS.  The Church does not create reality with her teaching, church teaching is based on the nature of reality.  Gay marriage, is, by definition, an oxymoron.  

The Constitution, so far as I am aware (and I admit I am no elitist lawyer with a fancy degree from an elitist school) does not grant any of the three branches of government the power to redefine reality based on the whims of pop-culture. Can you show me where the Constitution grants any of the three branches of government the power to altar reality based on cultural whims, trends, fads, fashions and the like?