Well, on your second point, I'm far in the minority, but I'm in favor of government recognition for polyamorous marriages of various sorts. The farther you move from the societal norm, the more individually contractually tailored your situation would have to be, but I don't in principle see why the reasons for marriage (financial cooperation, child raising, etc.) and the legal ramifications for it are less valid when more than two people are involved. But that's an issue for another day, and one that (at least so far as I see) is less of a problem of civil rights.
But to get to your main qualm, I object heartily: marriage is not at heart a religious institution, it's a social one. The fact is that historically most societies (including the US's main ancestors) have used religion do regulate their social institutions, but that doesn't mean that the institutions themselves are necessarily religious. Explaining the causes of natural phenomena (i.e. science) and encouraging people not to harm each other (i.e. morality) were historically the province of religion, but that doesn't mean that modern separation of church and state means the state should butt out of funding scientific research or preventing theft. People get married not just to sanctify their relationships in the eyes of God, but because living together in tight-knit units is a pretty good way to get by in the world--this happens in various forms across societies and religions, so I think it's hard to argue that the fundamental motive is a sacred one. (A nice counterpoint to your view, so far as I know, is the one taken by Buddhists: that marriage is primarily a secular, and not a religious, matter.)
Now, we certainly could debate whether, as Sarn argues, it's useful to gerrymander our dictionaries so that religions (Christianity) get to play with one term and governments get to play with another. But I take you to be arguing something more radical: that governments shouldn't regulate what I take to be a fundamental social institution. (It would be like saying, "Governments shouldn't have anything to do with the sale and transfer of goods: that's primarily a matter or religion.")