I know that you think that head coverings aren't necessary today, at least not the ones that are normally used. I have figured this out from some comments made in passing on other topics. I may just be missing it, but I can't find an answer directed specifically at this question. What are your thoughts on this matter?
There is only one passage in the Bible that addresses head coverings. That is 1 Corinthians 11:4-16.
Every man praying or prophesying, having his head covered, dishonoureth his head. 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. 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. 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. For the man is not of the woman; but the woman of the man. Neither was the man created for the woman; but the woman for the man. For this cause ought the woman to have power on her head because of the angels. Nevertheless neither is the man without the woman, neither the woman without the man, in the Lord. For as the woman is of the man, even so is the man also by the woman; but all things of God. Judge in yourselves: is it comely that a woman pray unto God uncovered? Doth not even nature itself teach you, that, if a man have long hair, it is a shame unto him? But if a woman have long hair, it is a glory to her: for her hair is given her for a covering. But if any man seem to be contentious, we have no such custom, neither the churches of God.
The subject of this passage is authority in the church. Paul is talking about men having authority over women. He is not mandating hair covering. He is using what was apparently a custom of the day to make a point. He then goes on to make the same point from nature.
That he is not mandating head covering in the church is clear from verse 16. Some translations have (perhaps intentionally) mistranslated this verse to read, “But if any man seem to be contentious, we have no OTHER custom, neither the churches of God.” Such a translation would indicate that Paul agreed with the custom, and indeed required it. However, the proper translation uses the word “such” instead of “other.” Never does the Greek word that is used here carry the meaning of “other.” Instead, Paul is saying that neither he nor the churches have a custom of requiring head covering.
To be fair, I must point out that some argue that Paul would not have written such a long discussion just to end it with a statement that everything he just said really doesn’t matter. They have a valid point. On the other hand, his point in what he has said is that even as they follow him they must remember that even he is not the ultimate authority. The passage is about authority, not head covering.
There is historical evidence that many early churches did adopt a practice of head covering for women. However, this usually took one of two forms. Either all women were required to be fully covered (much as Muslim women today wear the burqa), or only the unmarried women were required to veil the head. (This is opposite to the Jewish custom, that an unmarried girl may be seen without a covering, but a married woman must always be seen in public with her own hair covered.) Since the practice varied so greatly from place to place, it appears to have been more dependent on local tradition than apostolic mandate. In fact, those that required only unmarried women (virgins) to be covered appear to have allowed married women to go uncovered. This would show that they considered Paul’s discourse to apply only selectively. (One of the congregations, according to Tertullian, that accepted this practice was the one at Corinth.)
I have attended some conservative Churches of Christ (the label “conservative” being their own) that practiced women covering their heads during the assembly. I have been at some where it was optional but strongly advised. I have known others where it was required. One thing that stood out at these congregations was that neither practiced head covering like Paul talked about. Most of the women wore hats. Some wore what amounted to little more than a handkerchief on the head. A very few may even have worn a headscarf that covered the ears and tied at the chin. None of these head coverings meet the description in 1 Corinthians 11. Paul talks about being veiled, not just having something on the top of the head. Anyone insisting that women should have their heads covered must necessarily require that the covering be a full veil that not only covers the hair but also the face. Just try getting women in a modern American congregation to agree to that, no matter how devout they are!