We didn't, JessM We were a clean family, but we didn't agonise about maintaining hospital levels of cleanliness as people do now.
My mother was an excellent cook, but without any formal training, so no theory of bug control, just common sense. She washed her hands before cooking and prepared vegetables before starting on the meat, and she kept work surfaces clean as a matter of pride. We washed our hands after using the toilet out of disgust at not doing so, not because we thought we carried a million germs on our fingers.
We had a bath and changed our clothes once a week - washing everything by hand meant that throwing every garment into the laundry basket daily wasn't on. We washed daily, but deodorants had not yet been invented (or if they had, they hadn't reached us) so my father changed his shirt more often - but not daily. He wasn't in a manual job, so wasn't getting all sweaty and dirty. After school we changed into non-school clothes to keep school clothes for the next day.
We were not dirty or smelly, we were seldom ill, and we have all lived to a good age without serious illness (I don't include my father's cancer or my mother's heart condition)
Maybe there were fewer germs around in those days, or perhaps our exposure to them toughened up our immune systems so that they were more alert and dealt with them faster? Maybe all that playing outdoors made us more resistant?