I respectfully disagree. The Germ Theory of Disease did not fully take root until the late 1800s, less than 200 years ago.
A fine example is Ignaz Philipp Semmelweis who proposed hand-washing for doctors because he noticed that there were fewer miscarriages and post-labor deaths when doctors washed their hands between an autopsy and a birth. This was, for one, against commonly accepted theory at the time, as the Germ Theory had not yet taken serious hold or had much evidence for it. For two, his proposal was later rejected, doctors stopped washing their hands, and Semmelweis was later committed into an asylum.
https://en.wikipedia.org/wiki/Ignaz_Semmelweis
The CDC in the USA didn't even suggest hand-washing for doctors until the 1980's.
https://www.ncbi.nlm.nih.gov/books/NBK144018/
The 1980s represented a landmark in the evolution of concepts of hand hygiene in health care. The first national hand hygiene guidelines were published in the 1980s, followed by several others in more recent years in different countries. In 1995 and 1996, the CDC/Healthcare Infection Control Practices Advisory Committee (HICPAC) in the USA recommended that either antimicrobial soap or a waterless antiseptic agent be used for cleansing hands upon leaving the rooms of patients with multidrug-resistant pathogens.
"Washing our hands of it" is a relatively recent phenomenon, seriously. If it was "simply implications of an already established theory of cognition" I would think that we'd have a much longer, serious history of actual handwashing. For most of human history, humans have been absolutely fucking filthy. Early human history didn't even use soap for bathing as much as it was used for textiles. Even the Romans, known for bathing, used oils, not soaps. Further, before the Industrial Revolution, soap was mostly accessible to the aristocracy. The Industrial Revolution was... *checks notes... was 1760, about a hundred years before Semmelweis was one of the first people to propose hand-washing.
This is an extremely short time period for this behavior to be part of "an already establish theory of cognition." Whereas we have millions of years without serious hand-washing as part of human culture... which is where that established theory of cognition was developed... prior to handwashing.