Fermented foods and mushrooms can be good at fighting cancer precisely because they ramp up the immune system. In fact yeast is used as an adjuvant inside of vaccines for this purpose.
What's insane is that it is both known and not known that yeast causes inflammation by science. Used as adjuvant, used to "boost" immunity, yet not understood to be a cause of general low-grade systemic inflammation when in our food supply.
Opportunistic Strains of Saccharomyces cerevisiae: A Potential Risk Sold in Food Products https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4705302/