China still considers Taiwan to not be a country; go to a Chinese airport and at customs control it will have one line for "Chinese Passports" and one line for "International, Hong Kong, Macau and Taiwan Passports". Because, after all, Taiwan is not a foreign country. Whenever America sells weapons, ships, etc to Taiwan, this is always decried in the newspapers as "interfering with Chinese affairs". Saying this, the Chinese aren't stupid, and due to various cross-straits agreements it's not very difficult for Taiwanese to come to China or Chinese to go to Taiwan. There are several Taiwanese exchange programs at my university (I teach at a Chinese university). People are perfectly aware that Taiwan is controlled by a different government, and they know the history in a reasonably accurate way, it's just seen through a very nationalist framework. The Communists overthrew the weak, corrupt government of the KMT, who fled (with loads of gold) to Taiwan. The CCP is the legitimate government of China, and China is one nation. Taiwan is simply part of China ruled by a rebel government. However, this doesn't mean that most Chinese want to invade (some do). It's not that they wouldn't consider it legitimate to do so (it is, after all, part of China). But they'd prefer to slowly strengthen economic and co-operative ties so as to be united sometime in the future. It's not considered a particularly pressing matter. Of course, the Taiwanese know this. You might have seen the student protests on the news last year. They were protesting at a law that made it easier for mainland business to operate in China. They were worried that this would beholden them to China and thus they'd be forced in the future to unite.

One thing I've noticed however, that is very notable in its absence in the way Taiwan is presented, is democracy. There is no mention of the fact that Taiwan is democratic and China is not. It's presented as them wanting independence, not them wanting to be ruled by a democratic multi-party system. Now, many Taiwanese of course would like to be independent one way or the other, but others would probably be less averse to unification were China not a one-party state; this is not mentioned (except for the occasional mention that many Taiwanese, like many Americans, hate Communists. Those meanies). This was also noteable to me in the Hong Kong protests. Many asked me whether westerners supported the Hong Kong protests (I'm British), but they viewed it through the lense of Hong Kong residents wanting more independence from China (because they think they're better than us!), not Hong Kong residents wanting real democracy. Also, as a threat to basic law and order (many asked me if Britain would allow protests like this, but they didn't ask me how Britain would view the demands). The Newspapers for example, would say that the protests were "against the Basic Law and constitution", and never really explained the demands of the protestors.