Pragmatically speaking, going to war with China over Taiwan may very well be a bad idea since the possible consequences are very grave indeed. However, the idea that we should not fight to protect Taiwan because it really belongs to the People's Republic of China is based on a flawed understanding of the origin of Taiwan.

Up until World War II, the Nationalist Party was the nominal ruler of China. The Communist Party decided that it had a better way to do things so it tried to overthrow the Nationalist Party. When World War II began, the two parties decided it would be in their best interest to unite to fight against Japan, whom they hated even more than each other. When the war ended, the two parties resumed fighting with the result that the Communist Party succeeded in conquering all of China and ousting the Nationalist Party. The Nationalist Party retreated to the island of Taiwan.

Unless one believes that success in conquering a nation confers legitimacy on the victor, then if anything the Republic of China--Taiwan's name for itself--is technically more legitimate than the People's Republic of China. A decent historical analogy (though by far not a perfect one) would be if during the Revolutionary War the British Empire had managed to hold on to, say, South Carolina. Would we be correct in saying fifty years later that South Carolina had "seceded" from the United States of America?

Thus, it is in our best interest to treat the Republic of China as a separate entity from the People's Republic of China, and should it decided to fully "declare its independance", we ought support it as long as it is feasible for us to do so. There are worse reasons to go to war with the People's Republic of China than to prevent the annexation of an unconsenting populace.