Well, you have to remember that those people you're talking about don't really believe in a construction of gender that's separate from biology. And biologically, you basically have to be male or female. Of course the most basic level we are gendered is our sex chromosomes - men are XY and women are XX. The closest I guess you could really get to what you're talking about in terms of genetics would be XXY, which I think is down syndrome. But babies who are born with these rare accidental combinations rarely can really survive.

Basically, whenever people are born with genetic or other sorts of defects that give them ambiguous sex organs, the parents choose and doctors attempt to work with them physically in the hopes of giving them a normal life as one sex or the other. I imagine that with the current state of technology, they would usually decide it based on genetics - i.e., they'd try to get the sex organs to match the sex chromosomes.

Basically, I think it's a nice idea, but there is no conceivable way that a person could exist that the people you're talking about wouldn't find some reason to categorize as one sex or the other. There's just not biological support for someone half male, half female; I don't think you could ever have a case that would be so ambiguous that the law would actually have no idea or no basis to classify them as one or the other.