You wrote "Chinese Taipei is not a place name." and I hadn't noticed your name appear multiple times in the comments so I figured someone just genuinely didn't know Taipei is referring to the city rather than being some random Olympics-only moniker. And then with that second comment I just enjoyed being a pedant. Then when I did notice you had multiple comments I decided I should stop being rude because you weren't being rude.

There isn't really anything to disagree on. We (leftists) aren't oblivious to the fact Taiwan has (not full but significant) practical independence from China, and many of us are not even against them receiving de jure independence as long as they aren't allowed to host USA-controlled weapons. What I was trying to stress is that Chinese Taipei is a fine descriptor whether you support the PRC or ROC, since it's the Chinese city of Taipei, or even if you want Taiwan independence, it can still currently represent a team of Chinese people living in Taipei.

The hostility you see in the comments isn't because people want to deny Taiwanese their agency. Independence is stupid, and reunification under the PRC is absolutely what's best for the proletariat on Taiwan, and the rest of China, but it shouldn't happen without their popular support. What we're against is rocking the boat or god forbid, a war starting. The situation is currently workable for everyone. China gets their forced security guarantee because they legally own the land and the government on Taiwan is mostly left alone. The PRC doesn't blockade or sanction Taiwan over trade or financial issues. Every time they sanction them it's because of a direct military transgression and they've all been temporary. The PRCs whole strategy for reunification is just outpacing them in quality of life. Despite what western media claims, China is not being provocative. So stories creating the conditions for military conflict scare and anger us.

On the capitals. They're not equivalent to US-state capitals. They're supposed to be the centres of political power for the people who live in each autonomous region. While undoubtedly Beijing is the capital, or centre of political power for the whole country, that doesn't negate the regional governments' power. You said the biggest city is the capital, right? But the biggest city financially in the USA is New York, and culturally it's Los Angeles. And in terms of population they're #1 and #2 too. But the capital of the USA is the centre of political power. China aims for a higher level of autonomy than the USA does, partially because they're more committed to democracy, but also because the material conditions necessitate it. Beijing just isn't as good at administrating autonomous regions as they are themselves.