This Forbes article says (bold added by me):
If it was merely a question of Hong Kong in isolation, perhaps Beijing would consider some of the protestors’ demands … But Beijing will not and cannot consider Hong Kong in isolation, because of the implications for separatist movements in Tibet, Xinjiang, and in a different context Taiwan, which is already a democracy but which China one day hopes to incorporate back into the Mainland and which is therefore watching events in Hong Kong very closely. The Chinese state does not believe in displaying weakness and is not about to start now.
I cannot comment on Tibet and Xinjiang, but if the Chinese Communist Party (CCP) were primarily concerned about annexing Taiwan, they would into the protestors demands in Hong Kong. Refusing to give into the Hong Kong protesters makes it harder to annex Taiwan.
The protesters in Hong Kong are basically asking for the Chinese Communist Party to keep the promise made when the sovereignty of Hong Kong passed to the People’s Republic of China (PRC). The CCP is choosing not to honor this promise. So why should Taiwanese people expect the CCP to respect promises made to Taiwan, and how does breaking promises make it easier to annex Taiwan?
The power in Taiwan which is most inclined to accept annexation by the PRC is the Kuomintang (KMT), which is also Taiwan’s most powerful political party. Yet even Ma Ying-jeou, the chairman of the KMT (and current president of Taiwan) is officially siding with the Hong Kong protesters (Michael Turton’s cynical take on that) – short version: if the CCP is not respecting Hong Kong’s autonomy, it can’t be expected to respect Taiwan’s autonomy, which means that the KMT would not be able to hold onto power post-annexation, so why should the KMT accept annexation by the PRC?)
If the CCP were primarily concerned about annexing Taiwan, they would give into the Hong Kong protesters to show Taiwan that the PRC Can Be Nice. After all, they could stop being nice when the annexation is complete.
Taiwan is still independent of the PRC because a) they have their own military b) highly defensible geography c) the US military might get involved and c) the aftermath of a Chinese military attack on Taiwan might cause the CCP itself to lose power. I don’t think the CCP cares how many Taiwanese or Chinese would die or suffer, but they sure care about their potential downfall.
I think the CCP is most concerned with China, not Tibet, Xinjiang, or Taiwan. Most Hong Kongers (including most of the protesters) accept Chinese sovereignty, unlike Taiwanese people, so this is a conflict over governance, not sovereignty. If the CCP accepts democracy in Hong Kong, that will strengthen demands for democracy in other parts of China, and democracy could challenge the CCP’s hold on power. That is why the CCP will not give into the protesters’ demands unless it must. Not concern about Taiwan.