Because the issue they are protesting is extradition and the rule of law being maintained; HK has a western style rule of law, mainland has practically no rule of law to speak of.
I think the distinction trying to be made here is that Chinese, Hongkongers, and Taiwanese people don't see themselves as westerners. Posters aren't saying that they shouldn't fight for basic human rights, but rather that basic human rights aren't "western", they are human. We being westerners should be proud that we have laws like this, but that doesn't mean we need to impose everything western on others. It also doesn't mean that our fight for basic human rights is fundamentally western. Just the same way it isn't American, British, German, etc. They are basic human rights after all, and last I checked these people are still humans.
TLDR: basic human rights doesn't mean you have to identify as western.
TLDR: basic human rights doesn't mean you have to identify as western.