There are areas of Colombia that are a sovereign country because they are controlled by guerrillas. The same goes for Russian controlled areas of the Ukraine and Georgia.
What makes them sovereign countries with a right to be in the UN is the amount of recognition they get from their peers. I don't have anything against the Taiwanese, but they are embroiled in a conflict just like the previous regions I described. Until they solve those issues one way or another and gain more international recognition they will not be able to participate in the UN, the Olympics or other places as a country.