This standard was in use in all the Christian countries until about mid-1940s but only fully disappeared in the end of the 1960s.
To begin with, women were supposed to cover their head in public, which was a pretty universal rule and now disappeared completely, unless it's very cold/hot. Sometimes you will encounter it in more conservative churches, but outside royalties and Mennonites hardly anyone is doing it anymore.
Women were also supposed to wear skirts or dresses, but they started wearing pants during WWII when working in war factories (war situation was used to push a lot of societal change, just like "the war on the virus" now).
In countries like Mexico and some African countries only women of easy morals used to wear pants until about 1980s or even later, btw.
Skirts had to cover the knee when sitting and not to be extremely tight. You were expected to cover your elbows, too, the standard which gradually got relaxed in the 20th century. The necklines had to be not lower than 2 fingers under the collarbone.
Of course, we know that the upper class women disregarded the decollete rules already in the early 19th century and earlier, but at least, it was done during private parties in the evening, with bad light, and not in the streets during the daytime.
However, if you look at Medieval or Viking clothes (and we went to many a Renaissance fair), the styles weren't as different as what the Muslim ladies wore, except for the veil, but even those, though never mandatory in the West were more or less in fashion until the 20th century.
Somewhere along the way pretty reasonable early Medieval clothes changed into high court fashions complete with low necklines, corsets and crinolines and headcoverings into tiny hats, and then it all disappeared completely.
So unless we are Amish, none of us adhere to this modesty standard since we never routinely cover our heads in public as women. I'm adding this to show that I'm not trying to be holier-than-thou since I'm not following this minimal mid 20th century standard, either.
When I used to read the discussions on this topic, people would mention movie industry and how they would portray hip cowgirls in jeans, but I believe that the 20th century obsession with fitness had probably more influence. Somehow it became fine to run around in underwear if it was for sport or swimming. And then the underwear just kept getting skimpier and skimpier.
Of course, in Ancient Greece the Olympians competed naked. They were also heathen, and ladies weren't allowed to watch, they had the competitions of their own where men were not allowed in turn. (Free women had to fully cover their bodies in public as opposed to slave girls which indicated their status as sexually available.)
Some call it progress, some call it degeneracy...