The Government doesn’t take away from the religious rite of marriage, it can’t so your whole line of reasoning is fallacious.
Here's a little metaphor that should clarify the point:
RINOs don't take away from the message of conservatism, so they don't hurt the name "Republican" in any way, right?
You understand my point? The word and all that is associated with it is demeaned when some call an aberration by the same name.
Remember Rush's oft-used saying: "Words Mean Things". The word "marriage" means a union of two people, usually in a religious context. By giving that word over to gay "marriage" advocates to use, then we are letting them redefine what the word means.
It used to mean a commitment before God and all. Now it no longer means that, because the use of the word has been corrupted. Much like the very word "gay". It used to mean happy, joyful. Now it means homosexual - that word has been corrupted so that it can no longer carry the original meaning in any real way.
I do not want to see that happen to marriage.