If that is the case, then government should also have to stop giving benefits of any kind, including tax cuts, to married couples in particular. If it is none of the government's business, then it's none of the government's business. Though frankly I do see some purpose to a legal contract for keeping couples together except under strong enough circumstances that they're willing to go through the trouble of divorce and admit to breach of contract regardless of religion.
Marriage predates Christianity and is almost a cultural universal. The days in which it was founded in its earliest versions (nothing like those of today, or the traditional Christian ones for that matter) were in a context of religion and government being part of the same institution. Marriages have always existed for the purpose of social stability, people being forced by contract to take care of one another is the purpose that survives today as well as any children born or adopted. The really traditional versions were only partly that and mostly just a way of keeping track of whose kids were whose and how the clan property would be moved around. Actually most of the truly traditional reasons for marriage are obsolete in this day and age. It was not about love until fairly recently. I would suggest it's only purpose is to make two people take care of one another and any offspring. It does have the effect of building responsibility.
I could personally care less for whether government is involved in marriage or not. But to claim marriage is simply a creation of religion is false. It was created in a context where religion was government. And to think that what we call traditional marriage is really the oldest and most enduring model and that it has not changed is also false. Plus if government is going to get out of it, it had better be completely turned into a symbolic ritual and not an advantage for people in organized religious groups (even though I know most churches would still marry nonreligious people who pay them and don't embarass them).

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"Man lives in the sunlit world of that which he believes to be reality. But unseen by most is an underworld, a place that is just as real... but not as brightly lit... A DARK SIDE!"
-opening from Tales From the Darkside