I think it varies by hospital and situation rather than era.
My experience predates the folks the OP mentions and it was just a gown and booties over my shoes.
24 years ago, I don’t remember wearing anything special or even washing. The doctor wanted me to cut the umbilical but he didn’t ask if I was clean. Moments before the birth a nurse teacher showed up with a half dozen students who wanted to see a birth, so they all piled into the room with us, in their street clothes. I had to elbow student nurses out of the way to get a view of my son being born.