Head covering was never a dogma or doctrine. It was a discipline. Even in the time of Christ & St. Paul.
In order to properly understand it, it’s important to understand where it comes from and what it historically meant. Head covering actually is an ancient custom that was not exclusive to the Jews or Christians, nor was it specifically religious in nature. It was a form of modesty.
It is actually tied to a cultural tradition that linked the length of a woman’s hair to a sign of chastity.
When a woman had short hair, it actually meant that they were not practicing chastity. As late as the 19th Century, one of the punishments in Europe for prostitution was cutting the woman’s hair short.
Head covering (veiling), long before Christ, actually started as a way to make a woman’s hair appear longer than it really was. This would make her seem more chaste and desirable, or hide her if she had shorter hair for whatever reason.
Overtime, head covering took on the sign of modesty & chastity that was associated with long hair. By the time of Christ, it was a cultural sign of modesty & chastity.
Over time, the length of ones hair was no longer tied to chastity, but one’s age. Young girls had long hair, but it was OK for older women to cut their hair. But it still remained as a form of modesty. This lasted pretty much until the end of the 19 century. The World Wars & swim suits of the 20th century helped to effectively end the idea that head covering were a form of modesty.
When woman helped in the wars (whether in the Army, Navy or private sector); super long hair wasn’t practical nor was head coverings. Additionally, hats had already started to replace bonnets, veils, etc at Church. Then, as Hollywood movies started showing women in swim suits which show more and more parts of their arms, legs, neckline, and eventually navel, covering the hair became insignificant.
By the 40s and 50s hats were often worn by woman in public and outdoors, but men wore them too. Hats didn’t cover nor hide the length of the hair. So the original reason to cover one’s head (to hide the length of hair as a sign of modesty) was not longer being done. Women and girls were even wearing small pieces of cloth on their heads, which didn’t hide anything. Plus the once piece swimsuit was in full acceptance by the 40s and 50s with the bikini growing in popularity.
So, when society stopped viewing hats as a form of modesty but rather simply as a form fashion, and when some women were wearing tissues on their heads as a form of head covering, the religious purpose behind the head covering disappeared.
Because head covering no longer had any societal & cultural purpose, the discipline was removed.
NOTE: it’s important to understand that Church discipline can be changed, as the purpose of discipline is to help Christians live a Christian life in a fallen world. If the discipline means nothing or loses it’s meaning, and becomes simply an issue of obedience then it potentially hurts the Christian life.
So the whole point of St. Paul’s teaching was to dress modestly, which is something that many woman (and some young men) today have a problem with.