Un-PC as it may be, can we agree that enabling anyone to have a child out of wedlock--for the sake of some ill-conceived notion of equality or fairness--is wrong-headed?

Nope! Because I don't think that notion of equality and fairness is wrong-headed.

Even setting aside the "culture war" aspects, why is it in the interest of the State to mandate such a thing?

"Mandate" is misleadingly strong, right? It's the obligation of the State to provide its services equally.

First, MRH, these aren't "government services"; they are services that the government regulates to some extent. If you're saying that government regulations must be so absolute as to require private businesses to treat all people as if the circumstances of their lives (e.g., married vs. single) do not matter, I think you'll find it more difficult to pass future regulations. I also think, with regard to healthcare, that you'll further ensure that Rhode Island continues to exist under the problems of its current near monopoly.

Second, how is the marriage rule unequal or unfair? All women are covered equally by the regulation; they just have to enter into marriage in order to qualify for mandated coverage.

The state really shouldn't even allow fertility treatments for unmarried people, let alone require that it be funded. I know we can't stop all unmarried pregnancies, but we can sure stop these intentional ones with fines and jail, etc. Only a marriage has a right to conceive.