

Just over half of U.S. adults (52%) say they favor allowing public school teachers to lead their classes in prayers that refer to Jesus
Nationwide, a slightly larger share of Americans say they favor allowing teacher-led prayers referencing God (57%)
It’s right there in OP.
I think you’ve got it backwards. One of the lesser known, positive parts of the Cultural Revolution (which was primarily a horrible clusterfuck) was the Barefoot Doctors program, in which medical students were fast-tracked in education and sent out to the rural regions of China, which had never before had access to modern medicine. It was a very basic level of care, but it increased the number of doctors per person tenfold in the span of five years, and access to vaccines had a significant impact, increasing life-expectancy and reducing child mortality. However, because medical supplies in those regions were limited (and the scale of the program), the doctors were instructed to supplement care with traditional Chinese medicine (TCM). This allowed the program to be rolled out more quickly, and the partial reliance on TCM may have helped with public acceptance (since it was what they already believed in), but it had an unfortunate side effect that it legitimized TCM.
This program was phased out in the 80’s with China’s broader economic shift, towards privatization, while also moving away from TCM. The new policies made care less accessible and focused more on curing serious ailments rather than preventative care. China has made some efforts to address these issues, though I’m not well informed enough about their current system to weigh in.
A lot of the modern popularity of TCM likely comes from the time of the Barefoot Doctors program, because people remember their quality of life improving during that time and then declining later when the focus was shifted away from TCM, incorrectly attributing it to TCM’s effectiveness rather than the accessibility of care and focus on prevention. Which is to say, many of the people who believe in TCM may actually be nostalgic for the healthcare system implemented during the Cultural Revolution.