When I was in high school, the locker room had communal style showers, but there was no requirement to use them.
Swimming was a graduation requirement. If you did not pass a swim test, you had to do it (instead of other activities) for PE. No diving requirements.
We had gymnastics and had to do a routine on each apparatus! Unevens, vault, balance beam. I still remember most of my routines and I cannot believe we all did that with very little spotting and no one got seriously injured. (In my class, at least. I am sure there were injuries!)
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We did too. Spotting?
" Oh! Little 4 ft 70 lb. Suzy can catch you as you fly through the air! She’ll be sure to not take a giant leap backwards as your out of control flailing body comes hurtling towards her. " “But just in case she doesn’t-- aim your head at the 2 inch plastic mat on the floor.”
Barefoot.
I think it was more than case that I couldn’t believe what my kids were allowed to do in school, than they were shocked at what their parents had to do in school.
My children are shocked (frankly so am I) that their dad had to swim naked in High School! OMG! It is so so crazy that this was a thing (mid 1970’s).
When my mom got my kids laundry service at college so they wouldn’t have to do it themselves, some friends were shocked to learn that the reason my mom was so in favor of this was that in the 1950’s she also did not have to do laundry----because it was the “thing” for students to ship their laundry home!
That was also the requirement at the YMCA back in the day
Did they fear worn woolen swim trunks would dirty the pool water?
Before my time obviously, but supposedly male swimwear was considered less hygienic and risked contamination of the water.
It was 1975. Not 1905. The swim trunks were not made of wool!
My brother swam naked at the Y in the 1960s. Except Sundays were family days and everyone wore suits, even the less hygienic male suits. I don’t know how they did the locker room as I don’t think there was a female one since females weren’t allowed in the Y except on Sundays.
It was a big square building without windows. My Y has great big picture windows looking into the pool from the lobby but also from the outside to bring in light No naked swimming although there was an angry man running around the lobby in his speedo yesterday demanding the desk workers do something about the lifeguard who wouldn’t make the aquacize instructor let him swim laps in the middle of the class. He was quite scary and practically naked. (And he was wrong as lap swimming isn’t allowed during aquacize as they have to have more than one lifeguard if there are more people in the pool.)
I’ve seen my parents’ beach pictures, they had woolen swimsuits their mothers had crocheted (?knitted?) for them. In the 60s. They really hated them though. And I understand it wasn’t the pool but I wondered if it explained the reluctance for swimming gear 
The gymnastics unit and particularly the uneven bars were the stuff of my nightmares in junior high. I was terrified and did in fact fall off one time. Wearing my one piece snap front gym uniform. Early 1970s. Finally in high school we could wear tshirt and shorts.
This is how I got my one and only D in school (in 6th grade): by refusing to square dance. I don’t know what got into me. Why on earth did I think I could simply tell the gym teacher–or any teacher for that matter?!–a big ol “no?”
I do recall thinking that obviously nobody in New England should have to square dance, because we clearly knew nothing about it.
Someone should have told me I’d have a square dancing crush! I might have agreed to do it then! 
Definitely not the issue here. Maybe some unusual homemade thing. But By the mid 1970’s the suits were typical swim ware material like This. Poly cotton. Nylon. Vintage Swim Trunks Board Shorts Mens Large 36/38 Tan Orange Retro 70s 80s | eBay No wool. Vintage JCPenney Swim Trunk Lined Shorts Mens 48-50 Inseam Elastic Button 80s | eBay
I just can’t wrap my head around this . . . how would male swimwear be un hygienic??? More than being naked??
Something I can’t imagine my parents doing (I’m a HS 2025) was that back in Korea, they had to do these morning stretches in the “quad”. And these stretches are apparently so universal that a group of Korean adults did the stretches before the church tennis match last week, lol.
My grandfather had his left arm tied behind his back to force him to write right handed in Catholic school. It blew my mind as a kid.
When my left handed daughter started kindergarten at a Catholic school, they gave me an info sheet and one of the the questions was 'Anything else we should know?" I wrote ‘She’s left handed. Please leave her that way." Her K teacher, who was very strict about a lot of things (not a nun but could have played one on TV) had two lefties of her own at home so no problem with my daughter being left handed. The second grade teacher did as D was messy and couldn’t tear the papers out of the notebook easily; we had to have a ‘come to Jesus’ meeting over it’. Surprisingly, D is a pretty good artist and did learn to adapt to living in a right handed world.
It would have been a challenge to change my daughter to right handed writing. She’s not casually left handed as I’ve never seen her pick up a pencil or fork with her right hand. Never.