Dealing with the social and cultural situation of the first century, Paul let us know that our responsibility is to be conformed to Christ and not to our culture.
Romans 12:2: And be not conformed to this world: but be ye transformed by the renewing of your mind, that ye may prove what is that good, and acceptable, and perfect, will of God.
In dealing with the social issues of the Greek world of Corinth, the hairstyles and wearing of veils and shawls was a way of letting society know what type of person you were. Women who did not wear veils were looked upon as less than moral in their character. Remember, the city slogan of Corinth was “Everything is permissible.” We tend to forget that Corinth, being a critical port city, was the most carnal, debaucherous city in the Roman world with 1,000s of prostitutes, who wore their hair down and cropped it off.
So, what Paul is dealing with is how the world judges everyone by their outward appearance. Our responsibility is to be sure to abstain from all appearance of evil, so that the world can see Christ in us.
1 Thessalonians 5:21-22: Prove all things; hold fast that which is good. Abstain from all appearance of evil.
Verse 3 gives us the definition of how to understand verses 4 & 5. God’s divine administrative order is given.
1 Corinthians 11:3-5: But I would have you know, that the head of every man is Christ; and the head of the woman is the man; and the head of Christ is God. Every man praying or prophesying, having his head covered, dishonoureth his head (Christ). But every woman that prayeth or prophesieth with her head uncovered dishonoureth her head (her father if unmarried or her husband if married): for that is even all one as if she were shaven.
It is imperative to gauge our impact in our community for Christ by our separation from the world, and unto Christ. It is not just the outward appearance that matters. It is the lifestyle we live.