I have not been as meticulous as you, but grew up with similar rules. I've been thinking about this recently, and I wonder how much is related to the 1918 pandemic.
My mother's mother was Queen of Ironing. She ironed everything, sheets, underwear, socks ~ even the occasional grilled cheese sandwich, (wrap it in foil, iron both sides!) When asked, she would say 'for hygienic reasons'. She would get upset if you pressed her on it.
I suspect it was related to the fear of germs from 1918. Think of the news briefs we get. People in 1918 didn't have that, there were no news broadcasts. They had daily, perhaps twice daily in cities, newspapers. They were on their own far more than we are. I have great respect for past generations.