It isn’t altogether clear that Paul was talking about ladies’ hats in 1 Corinthians 11:1-16. Whatever the custom of head ware the Corinthians practiced, and the women were abandoning, cannot be directly translated to Western, Americanized church life.
Like other scripture passages that address the role of men and women in church life, this passage has created a plethora of opinion — learned and otherwise — about Paul’s point and how it does related to modern believers.
Perhaps the best approach by commentators is to view the problem Paul addressed in terms of the eschatology of the participants; that is, whether the men and women in Corinth held to an under-realized, already/not yet, or over-realized eschatology.
Essentially, Corinthian society had adopted certain external demarcations to accentuate and confirm the differences between men and women. One of them happened to be, apparently, that women covered their heads (or held up their hair) and men neither covered their head nor let their hair grow long, especially in terms of corporate worship.
The Corinthian women that Paul addressed had begun to abandon some of these distinctions. When the kingdom comes in its fullness, such distinctions will be moot, as when Jesus said that in heaven there is no marriage, and when Paul said elsewhere that in Christ there is neither Jew nor Greek, neither slave nor free, neither male nor female. But for now, such distinctions still matter in church life, and to hold otherwise is to fall prey to over-realized eschatology.
Over-realized eschatology tends to blur valid distinctions for present kingdom life in other ways, as well. Some believe that distinctions between spiritual giftedness are no longer relevant, or that distinctions between shepherds (pastors) and flock (congregation) are no longer relevant, or that — like the Corinthians — the church should hold to complete equality of role, function, and position as between men and women.
These beliefs are illustrated when believers suppose that the opinions of all believers are equally valid, and that all believers are qualified for each role in the church, because each has the Holy Spirit. They are illustrated when believers adopt an extreme priesthood-of-believer approach and resist submission to the teaching of the shepherds. Much of the problem stems from the inclination to apply Western political and social perspectives to the church.
What the church should take from this teaching is that during our time on earth, while the kingdom is not yet fully consummated, there is still a place and function for distinctions between males and females in church life, and that the attempt to do away with them is premature.