Anyone who thinks gaydar is just about picking up on stereotypes doesn't really understand gaydar. It's not about obvious attributes that play into stereotypes. Rather, gaydar is about the subtle clues in language or personal style, or nearly imperceptible aspects of behavior or personality that are invisible to anyone not finely attuned to detecting them.
It takes zero insight to spot obviously stereotypical things; it takes finely tuned gaydar to discern between the meticulously groomed, polite, slightly effeminate but 100% straight man and the slovenly, sports-loving, "frat bro" who is actually gay. If anything, it requires ignoring stereotypes and focusing almost entirely on subtleties and almost imperceptible details.
It's also worth noting that gaydar isn't a party trick -- it evolved as a life-or-death protective measure, from a time when making your sexuality known to the wrong person was very likely to get you killed. That is still the reality in far too much of the world, even today. So the implication that gaydar is not relevant any more could be seen as coming from a place of western privilege. Something worth thinking about.