Summary
There is a great deal of controversy surrounding soy foods, mostly due to their isoflavones which can bind to estrogen receptors and affect thyroid hormone.
There is significant evidence that eating moderate amounts (one to two servings per day) of traditional soy foods, whether fermented or not, can reduce the risk of prostate cancer and can lower LDL cholesterol.
People have been concerned that moderate amounts of soy could increase the risk of breast cancer or be harmful to women with breast cancer, especially if their cancer is estrogen receptor positive. However, the research to date has been quite reassuring, showing mostly benefits for breast cancer prevention.
Everyone who eats soy should make sure they are getting enough iodine. People with hypothyroidism might need their synthetic thyroid hormone dosage adjusted if they start eating more soy due to the possibility that soy might interfere with it. There is some concern that eating soy could push some people with subclinical hypothyroidism into overt hypothyroidism, so limiting soy for such people might be a good idea.
Soy infant formula has been shown to be safe except possibly for infants with congenital hypothyroidism, whose thyroid function should be monitored. Soy formula is not intended for pre-term infants.
While one observational study found that tempeh was linked to better cognition in older people, tofu has been associated with worse cognition. This is most likely due to confounding variables, including tofu being processed with formaldehyde in Indonesia. Many clinical studies have found that soy increases cognition. Unless you are in Indonesia, you do not need to worry about tofu harming cognition.
Some soy meats or foods containing isolated soy protein are processed with hexane and there may be small amounts of hexane residues in the final product. It is not known if this is harmful, but it might be a good idea to use soy foods from companies who do not use hexane in their processing methods (linked to below).
The phytates in soy can lower the absorption of calcium, zinc, iron, and magnesium. However, you do absorb these minerals from soy foods and eating moderate amounts of soy should not cause deficiencies.
At moderate amounts, soy does not cause feminine characteristics in men. At high amounts, as in twelve servings a day or more, a small percentage of men who are particularly sensitive to soy might develop tender, enlarged breast tissue.