The complaints about nude physicals at my school came from conservative religious families.These are, as so often in such matters, the Usual Suspects.
The last time my mother took me to the pediatrician was when I was 15 (I didn't go to the pediatrician anymore after that). Back then, it was normal for children to go to pediatricians with their parents. I didn't like the fact that my mother was present in the office. I felt treated like a little child then.I especially didn't like it when I had my underwear down to my knees. There was always a doctor (a woman) who examined my genitals. My mother always "reminded her" of this at the end of the examination. Back then, it was normal in many families for children to be undressed in the presence of their parents. It was believed that children should not be ashamed of being naked in front of their parentsWhat embarrassed me wasn't the fact that my mother saw me undressed. I was embarrassed by the fact that I was being examined in the presence of my parent like a small child. I was less ashamed when I was that age and undressed only in front of my mother, which happened quite often (spanking, enema, body inspection).
By the time my younger son was about 11 I would leave the exam room so him and the doctor had some privacy.