Such marriages are one of the newer hot-button topics and you can find a wide range of opinion about them, but that's not the point here: it's not hypothetical; such marriages do already exist.
In the past, the Census -- yes, the honored, respected, methodical sugar daddy of the Hollerith card United States Census -- has diddled the data. Fudged the stats. One year, they just "unmarried" all same-sex couples found (and one could argue that is exactly what DOMA obliges the Feds to do; once again, I remind readers this is about what is, not how you'd like it to be). Another decade, they handed out on-paper sex-changes to make things add up, which must've come as shock to any of the so-designated if they found out.
Where am I going with all this? Just here: Show me where the devil it says in the Constitution as amended that the Census gets to ask anyone about how many bathrooms their house has, what race they are (other than "Indian not taxed," anyway) or if and to whom they are married? You cant; it doesn't.
Let's have a look at the document. In the 14th Amendment, para 2., the earlier nasty compromise is amended to this:
Representatives shall be apportioned among the several States according to their respective numbers, counting the whole number of persons in each State, excluding Indians not taxed. But when the right to vote at any election for the choice of electors for President and Vice-President of the United States, Representatives in Congress, the Executive and Judicial officers of a State, or the members of the Legislature thereof, is denied to any of the male inhabitants of such State, being twenty-one years of age, and citizens of the United States, or in any way abridged, except for participation in rebellion, or other crime, the basis of representation therein shall be reduced in the proportion which the number of such male citizens shall bear to the whole number of male citizens twenty-one years of age in such State.
Then a bit later on, we got the 19th Amendment (about which I still have my doubts):
The right of citizens of the United States to vote shall not be denied or abridged by the United States or by any State on account of sex.
Congress shall have power to enforce this article by appropriate legislation.
Help me out here -- did it say "marital status" or "percentage with indoor plumbing" in there? Or did it just say, "counting the whole number of persons in each State, excluding Indians not taxed?"
They'd have a lot easier time of it in Washington City if they'd just read the instructions.
But you already knew that.