Chinese culture is as capable of tolerating diversity as any other - take a look at Taiwan. Same sex marriage legalized last week.

The political institutions in mainland China, on the other hand, are motivated by nationalist tendencies to foment hatred to Other.

Aaaand they definitely jail people just for religious group membership so they discriminatory as fuck.

Eh, I don't think most people think of Taiwan when they say "Chinese culture", especially in the US. The mainland and Taiwan are far enough diverged that they should be considered two fairly distant clades.

Taiwan is 100% Chinese culture.

If people don't think of Taiwan when they say "Chinese culture" perhaps it's simply because they don't actually know about the topic.

I should clarify, this is fair. When I say "Chinese culture," I mean in the Epic sense - five thousand years of Chinese heritage and cultural tradition, mushed together from all the provinces and colonies. It's not a very well defined thing, so your comment is quite fair. It includes things like the use of the Han writing system, a similar linguistic heritage, certain medical beliefs, a smorgasbord of culinary traditions, a flavor of bureaucracy, etc.

With this in mind, the PRC has slowly been eroding many aspects of this "traditional" Chinese culture, such as the high respect paid towards intellectuals, teachers, and philosophers (through the use of reeducation camps and propaganda). Meanwhile, Taiwan starts to discover new things about the natures of traditional Chinese culture, like its compatibility with quite liberal concepts (same-sex marriage, as an example).

Many Taiwanese people will say their cultural identity aligns with the thousands of years of Chinese history, while rejecting the last 60 years or so of change on the mainland.

Nowadays someone might say "Chinese culture" and be taken to mean things like "tendency towards tyrannical capitalism masked as communism" or "tendency to imprison people for thought-crimes," so I appreciate you bringing this up.