This post raises a thought-provoking conversation for pastors to consider. I agree in principle with Doug Wilson that it's better for non-Christian*, cohabiting couples to get married than to continue cohabiting unmarried. I also agree with those who note that this creates an opportunity for a conversation about marriage and the gospel. (Well, a couple people sort of reference the gospel, at least.)
But there are other issues that no one addresses and only Al Mohler even approaches. For example, why would a cohabiting couple even desire marriage by a pastor? Do they want a "church wedding"—a Christianized ceremony conforming to societal expectations and endowed with a pastoral imprimatur? Is that something a pastor really wants to offer couples in an ongoing state of unrepentant sin?
My dad's a mayor and (at least so far) marries everyone that the law allows. Couples leave that ceremony with no illusion that they have the blessing of a religious sacrament. I think I could marry a non-Christian, cohabiting couple, but only if I'd thoroughly persuaded them of that same fact.
*The post doesn't explicitly address whether the couples are believers or not, and some of the commenters unhelpfully increase that ambiguity.