Since the Law has not been abolished, neither has head covering, aka the tzniut that wives must wear, which is a symbol she is married, hence why Paul says, "it is a symbol of authority over her head". For when a woman becomes married, she comes under the authority of a husband, due to the curse against Eve when she transgressed, "your desire will be for your husband, and he will rule over you". As such, when Rebekah first saw Isaac, who she was going to marry, she "veiled" herself, which is the tzniut. However, if a wife does not want to wear a head covering, then she must shave her head and remain shaven, because in addition to the head covering, a wife with a shaven head is another symbol of marriage, hence "...if you see any captive woman, you may take her as a wife. You shall shave her head...". If a wife does neither of these, then she is in disobedience to the commands of God, and not only her, but also those who approve.
1Co 11:4 Every man praying or prophesying, having his head covered, dishonoureth his head.
1Co 11:5 But every woman that prayeth or prophesieth with her head uncovered dishonoureth her head: for that is even all one as if she were shaven.
1Co 11:6 For if the woman be not covered, let her also be shorn: but if it be a shame for a woman to be shorn or shaven, let her be covered.
1Co 11:7 For a man indeed ought not to cover his head, forasmuch as he is the image and glory of God: but the woman is the glory of the man.
1Co 11:10 For this cause ought the woman to have power on her head because of the angels.
1Co 11:13 Judge in yourselves: is it comely that a woman pray unto God uncovered?
1Co 11:14 Doth not even nature itself teach you, that, if a man have long hair, it is a shame unto him?
1Co 11:15 But if a woman have long hair, it is a glory to her: for her hair is given her for a covering.
The covering is not a veil,but it is the hair on their head.
It is a shame for a man to have long hair,and even nature testifies of this,and he should have short hair for he is in the image of God,so Jesus would of had short hair.Samson had long hair,but after Adam and Eve sinned nobody was in the image of God until Jesus came manifest in the flesh.
A woman should have long uncut hair,and if she cuts her hair it is the same as if she were shaven,whether she cuts it 5 inches,or one millimeter,and would put her self in the position of a man,out of the authority structure of God,the same with a man having long hair.
In the 1960's when the youth,and younger adults were rebelling against authority,what did they do,the men grew their hair long.
Some will say legalistic,as if God cannot have any form of standard among people,with the attitude with do not tell us what to do,even if it comes from God.