Sounds like our backgrounds are very similar. Both of my parents grew up in big families---with few bedrooms and only a single bathroom as well---so at least seeing family members of the same sex in any manner of undress was no big deal. Additionally, they grew up in semi-rural environments...so at least with the guys, going to the "swimmin' hole" naked was no big deal, either. I guess that they just carried that attitude forward...and I'm glad they did because I'm not all hung up on hiding myself. And, I had a great relationship with my dad and brother. It was a lot more open between us shootin'-the-shit while we were shaving/showering.Exactly how it was in my house.
My father grew up in a family of 10, 4 brothers shared one room, one bathroom for everyone. Little privacy there I would guess.
Then, like your dad in the Navy, my dad was in the Army in WW2. No privacy there either.
So growing up, sharing the bathroom with my dad was just natural. My sister got to use the other bathroom which was fine for me because I wanted to be with my dad in the morning.