This policy could lead to awkwardness. One could have some fun with this, but I’m wrestling with a philosophical question: to what extent should society be obligated to accommodate people’s eccentricities? At one extreme, I think we can all agree that a guy calling himself Napoleon should not be addressed as “your highness” (or whatever the etiquette at the time required). On the contrary, it might well be morally incumbent upon us to disabuse him of his delusion.
Try running that argument on men calling themselves women. (There’s a reason this blog is anonymous.) OK, but what about genuine women who happen to look like men? When such a woman insists that she really is female, who gave anyone the right to dispute that based on her outward appearance? And then there are the various chromosomal anomalies (such as of the XY-female type).
In short, who gets to determine the essential identifiers of a property, such as gender? If you say it’s always the individual, you’re stuck with accommodating a guy who feels like a woman on Mondays and Thursdays. If it’s always the society, that woman who looks like a man is out of luck.
This feels like one of those cases where the vast majority of instances are clear and unambiguous, yet no clear-cut rule seems to work.