Well, the fact that you take a stance on the subject's truth indicates that you do care. :) Taiwan's place in history is about as muddled as Palestine, Tibet, Ireland, and others, sometimes less, sometimes more. Some people take one side, some people take the other side, while I've found that people who don't care don't actually take a stance.
One thing that Taiwan (i.e, the Republic of China) and China (i.e, the People's Republic of China) can agree on is that the island of Taiwan is part of China.