I happen to be a Fujian native (Hokkienese). The word Min-nan actually means Southern Fujian while Taiwanese mostly originated from S. Fujian speaking the same vernacular.
It's understandable some prefer to call their dialect as Taiwanese rather than Min-nan. By so doing they assert a 'new' identification, different from their 'roots'. All about politics - when pro-independence force came into power they tried to erase traces related to "China" such as textbooks, names of museums, roads, squares. When the opposition regained power they reversed all that...
Motives in essence quite like your Mumbai vs. Bombay, Kolkatta vs Calcutta, or Tamil Nadu vs. Madras (correct me if wrong)
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Another insight I gained from this thread is how China and India are polar opposites of each other in many more aspects than I had known before. Not only in terms of government policy, but also in terms of how people think.
Not really. U have English (that's why Indians across the country can interact on DFI) that basically functions as Mandarin.
And a common language/script was enforced in China probably dated back to Before Christ (Qin Dynasty). In fact many Mandrain-speakers find Cantonese easier to learn than many other dialets with similar linguistic roots.
By the way Hong Kong or Macau irrelevant to the 'banning' or 'regulating' as SAR (Autonomous Regions)