Depends on what interests are linked to the sides.
In the case of Taiwan, the PRC is the main worldwide producer of cheap goods, so nobody wants to antagonize them, but at the same time many countries have interests in outsourcing and importing from Taiwan, so they end up in a "low-key recognize" situation.
In other cases... some countries have a direct strategic interest in one side, some have economic relations with one side but not the other, and others just don't care.