People get over being painted with offensive stereotypes because they don't have the social power to combat them - they don't have any choice but to put it aside and carry on. It's not because they really don't mind being treated that way. Hello! Do you mind if I call you a guy swimming in White male privilege? I'll bet you do mind, even though there is more than a grain of truth to it.
Just because there is a pervasive stereotype has no bearing on the actual truth of it. It's merely a cultural narrative that serves a purpose for some group of people - quite often to marginalize or shut up some demographic that is asking for better treatment - which is what this entire story is about.