I play characters of both genders but bias towards picking females, probably because I am a female. When I do pick a gender, it is based on the backstory I drew up for the character and even then gender is usually not that big of a factor for me unless the game takes place in a world where there are strict gender roles that I want to break or conform to. I wonder if the females I know who play games tend not to mind playing males while males I know (not all of course) do tend to mind playing females because many of the games we ladies were exposed to in our youth usually only allowed us to play as boys. Playing an opposite gender was normal; it only rarely bugged me but I was much more interested in playing the game than nit picking over not being able to play a girl. Since guys typically were able to play their gender, they did not have that experience and it may be why some guys balk at the idea of playing a girl or why guys who play girls are sometimes scoffed at. I think there are other contributing factors, but males being the typical gender you had to play could be one of the factors. It is a bit tangential, but I remember me and two of my female friends as kids being so thrilled to play Tomb Raider since we could play as a girl. It was amazing to us that the main protagonist and person you got to play wasn't a boy like usual.
