In Joseph Henrich's book The secret of our Success he discusses the importance of culture as a factor in the rise to success of Homo sapiens.
In chapter 14 he specifically discusses examples where culture has large effects on people's biology. The chapter includes a discussion about placebos and nocebos (the opposite to placebos: inert things that make you feel worse). He notes:
...the action and effectiveness of a placebo often depends entirely on how much faith a patient puts in a particular placebo or medical treatment. The more you believe it will work, the more it may actually work...
The same, he argues, applies to nocebos. He quotes a particular example based on Chinese astrology. In short, people born on particular Chinese years are thought to be susceptible to diseases connected to the spirit of that year.
This is testable:
The prediction is that the combination of getting a particular disease and being born in a year that is believed to be associated with the relevant symptoms or organs of that condition will result in an earlier death. Chinese Americans with an unfavorable disease–birth-year combination can be compared against both Chinese Americans with different disease–birth-year combinations and with white Americans with the same diseases but who presumably don’t put much weight on traditional Chinese astrological beliefs.
And he claims it seems to be true for example for bronchitis, emphysema and asthma (associated with the lungs and therefore unfavourable in birth years ending in 1 or 0):
Looking at all Chinese Americans, females lose four years of life and males lose five. Since many Chinese Americans may no longer put much stock in traditional Chinese astrology, it’s worth looking at those living in the larger Chinese communities in Los Angeles and San Francisco and those born in China, because these populations are more likely to have retained traditional beliefs. For men, the picture doesn’t change much, but the years of life lost by women go as high as nine years. Similar patterns emerge for cancer and heart attacks.
So, basically, the death rate is higher for some Chinese groups in years though to be unfavourable according to Chinese traditional astrology.
He also points out that these observations clearly don't apply to Americans who don't have any cultural background in Chinese beliefs.
But this sounds like a pretty significant effect (but then, so is the placebo effect). Can the effect of belief in tradition have such a strong effect on mortality?