Your use of the word "let" or "allow" is misleading. No liberties are being denied. The individuals are free to pursue happiness.
The state's definition of marriage, fixed for centuries, follows the traditional definition. The question is whether the state's definition should be changed. Why should it?
(Having an "alias" called civil unions is almost the same thing as changing the definition, if all legal structures of marriage apply to civil unions as a matter of principle.)
I certainly don't think my marraige or anyone else's is under attack because the women down the street got married. My marraige is strong and doesn't need defending from homosexuals.
My main concern is that I know this profound change will affect the next generations. I cannot predict what that change will be, but noone has yet enunciated a satisfying reason why the change is needed.
If such a law was proposed, I would debate against it, and the law would then be passed, or not. This is not what happened in my state (Massachusetts) - four people with robes "passed the law" - and I am very angry about that. Do you blame me?