Taipei Times - archives
Basically, I think this term has come to take on new importance in Taiwan. Here's a little backgrounder before I get to my point:
“People from an ethnic group generally wish to be called by the name they give themselves, if possible in their own language. This preference has gained importance recently as a means of avoiding ethnic discrimination.”
“An exonym is a name for a place that is not used within that place by the local inhabitants, or a name for a people that is not used by that people. The name used by the people or locals themselves is an endonym or autonym.”
I think you can see that the same kind of thing has happened with 山地人 or Mountain People which is now Native People in Taiwan 原住民.
What's interesting about Tai-Ke is that it was once considered a bad word used by people outside the people in this societal group. With this very group now using it and embracing it, they have taken away the negativity of the word and have empowered themselves by making it their own.