Why can countries officially recognise both the Democratic People’s Republic of Korea and the Republic of Korea as different political entities despite them both claiming to be the true Korea, but not the People’s Republic of China and the Republic of China, instead having to choose a side?
They can, it is just that if they do that, the PRC will sever diplomatic relations with such a country. Why that is so, you would have to ask them… neither of the Koreas has such a policy.
The situations are also not exactly the same: out of these, all are members of the United Nations except the Republic of China.