Historically, the transgendered were swept under the rug in Western society and we're left with hopelessly inadequate naming conventions. Some cultures have come up with extra genders in order to accommodate the transgendered and this sort of question is moot.

Working within the present naming conventions, we can develop a simplified model. Suppose there are two sexes (M and F) and two genders (M and F). To every person we can associate an ordered pair where e.g. (M,F) would denote someone who is biologically male but identifies as female. Mathematically, we have a map F from the set of humans (H) to the cartesian product {M,F} X {M,F}.

The question at hand can be stated thus: suppose we wish to define a projection operator p: {M,F} X {M,F} to {M,F}. Is it better to project onto the first coordinate or the second? In other words, should we associate (M,F) with M or with F?

Projecting onto a coordinate loses information. This is unavoidable. The answer will depend on which bit of information we consider more important. That, in turn, depends entirely on our values. My own view is that if we accept the legitimacy of being transgender (as opposed to considering it a mental defect), then one's present self-identified gender is far more pertinent to daily life and so deserves priority. Changing our conventions would be ideal, but in the meantime we have to deal with accidents of history.