Ever heard of hermaphrodites?
There's no such thing as fixed cellular level sex...People can have all kinds of chomosome combinations. Sex is a basicly a combination of basic biological structures and hormones at work. Gender is much more.
I'm aware of what hermaphrodites are. Yes, they are both sexes, but they also have cellular representation of such. As for polysomial conditions, the biological representation of these in humanity is very small, and even then, it's hard-wired, and not a sudden onset matter. There are indeed disorders that make you a sex neither purely male or female, but these are present from birth, and no procedure can produce their cellular form.
"Gender", as it is modernly defined, is, frankly, a load of wish-fulfillment bollocks. It's the concept that someone's opinion actually means jack squat in terms of influencing veracity. It is but a desperate grab at control where none exists, so people can feel less like pathetic and helpless waifs.