I would just like to comment that in pre-Vatican II days, when women all were required to cover their heads at Mass, almost no one wore mantillas.
I grew up in the Northeast, and my husband grew up in the South. We compaired our recollections, and we agreed, no one wore mantillas.
If you saw them it was almost always on someone who was born somewhere in Europe, and even old foreign women seldom wore them.
Mostly all women wore hats, scarves, or veils (just netting with little pieces of velvet on them like little bows or balls), what was called “babushkas”( large and small scarves folded in a triangle and tied under the chin) were very popular.
Later when I was in high school the school requirement for chapel was the small round “chapel cap.”
Again, the mantilla thing is something novel and begun in recent times by people considering themselves “traditional,”** only mantillas were never a tradition in this country.**