I think the PRC's policies attacking religion in the early years only to backtrack in the 2000s severely hurt Chinese culture.
It led to the demise of Chinese folk religion / Chinese buddhism (which hurt cultural ties with the diaspora) and the rise of Christianity.
It's a phenomenon that's so bad that many Chinese use "jesus" for figure of speech in daily life, instead of something like "老天爷" or "佛祖". In many Chinese movies and shows, scenes with religion also often use christian imagery rather than traditional Chinese religion.
No, PRC is not unique in suppressing religion. All Chinese dynasties have tried to "suppress" any folk religion that is not in line with the state. Shang dynasty was heavily religious in the similar way as the Aztec (human sacrifice, Shaman religion), the following Zhou dynasty removed the practice. Qin suppressed everything except legalism. The following Han installed confucianism as the state ideology (together with legalism) which lasted to 1900s. During that 2000 years, the state has supressed all sorts of religions whichever was percieved in threatening the state power.
Read this
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These are the three times when buddhism was the receiving end. Note, buddhism were practiced by many emperors of the three dynasties , but whenever the emperors sensed a threat, they don't hasitate to supress their "own" religion.
There are also Taosim being supressed, search for it.
Also read the history of folk religion of "white lotus", the Ming and Qing dynasties were not tolerate either.
Religions regardless foreign or Chinese are part of Chinese history and have lots of impact on Chinese culture, but they are not a defining part of Chinese culture. It is a appendix that is left untouched when it is not harmful, but will be removed if it got the body trouble.