I think this is where our disagreement is found most keenly. In my experience this is a performative reaching out done in a settings where younger people aren't really considering what it's like to be themselves and shed societal expectations. They aren't just 'being me' - they are considering what sort of 'me' is best reflected in society at the moment and building this from the outside in. That's why I think the movement is so prevalent amongst the young when it should be (in theory at least) equally distributed across society.
To use your analogy, sometimes its better to be in the Azores, because New York and London aren't where the cool kids are to be found. That doesn't mean there aren't people in the Azores who prefer it there, or even people who natively belong there - it's just become a package holiday for gender-tourists. Like most package holidays, it's not going to be good for the island. What they really want to do is bring a bit of the Azores culture to London or New York when they come back.
To my mind the Azores is intersex, which tends not to feature in the discussion at all very much.