In every church that I have been a member of, over 40 years, this has been ignored. It was not ignored 45 years ago — as a young child I recall my mother and grandmother and aunts all had hats that they wore to church, along with their “Sunday Best”.
Those were the days when men wore suits. To church, most days. Paul is arguing from the natural law here, and this teaching will really offend feminists.
1 Corinthians 11:2-16
2I commend you because you remember me in everything and maintain the traditions just as I handed them on to you. 3But I want you to understand that Christ is the head of every man, and the husband is the head of his wife, and God is the head of Christ. 4Any man who prays or prophesies with something on his head disgraces his head, 5but any woman who prays or prophesies with her head unveiled disgraces her head — it is one and the same thing as having her head shaved. 6For if a woman will not veil herself, then she should cut off her hair; but if it is disgraceful for a woman to have her hair cut off or to be shaved, she should wear a veil. 7For a man ought not to have his head veiled, since he is the image and reflection of God; but woman is the reflection of man. 8Indeed, man was not made from woman, but woman from man. 9Neither was man created for the sake of woman, but woman for the sake of man. 10For this reason a woman ought to have a symbol of authority on her head, because of the angels. 11Nevertheless, in the Lord woman is not independent of man or man independent of woman. 12For just as woman came from man, so man comes through woman; but all things come from God. 13Judge for yourselves: is it proper for a woman to pray to God with her head unveiled? 14Does not nature itself teach you that if a man wears long hair, it is degrading to him, 15but if a woman has long hair, it is her glory? For her hair is given to her for a covering. 16But if anyone is disposed to be contentious — we have no such custom, nor do the churches of God.
via Daily Lectionary Readings — Devotions and Readings — Mission and Ministry — GAMC.
Why the offence? Consider the highlighted text. Paul is going back to Genesis, Women are men’s helpers, they are there because it is not good for a man to be alone, and Paul says that this position under authority is shown symbolically by veiling.
Why the offence? Because it goes against our sense of casualness. Look at the context (I link to the lectionary for a reason). The following bit is about people not sharing at the meal — and Paul recommending that the meal not be for sustenance, but for fellowship. We should eat at home, then come to celebrate. Which is why one loaf and one cup are enough. This confronts me and my habit of wearing jeans everywhere. Worship is serious. I need to consider wearing a suit.