In the 1990's New York City was ruled by mayor Rudy Giuliani despite the city being solidly Dem federally. ... Obviously a MAGA Republican can't win it back...
Ironically shows how manipulative political mass media is, since "MAGA" is quite literally Giuliani's agenda and being pushed by a New York Republican. Trump arguably embodies the Giuliani ethos better than anyone in politics today. To the extent their tagline is applied to fringe figures like Gaetz, Boebert, Greene, it’s because they’re a lot more like Trump and Giuliani than their district would previously have elected.
As to your last question, there was a lengthy discussion on this recently that you can find via search.
