Calvin and many other commentators say that the meaning of this verse is that we do not have the custom of being contentious, so we are not going to be argumentative about such things. Others put it differently.
There is still a language spoken by dress. Men, do you go about in public with tight fitting garments, tight fitting garments which a worldling would adopt deliberately to impress the world, or the womenfolk, concerning his body shape or fitness. Are Christian people doing that, dressing sensually, using exhibitionism, wearing tight things to show off, to vaunt imagined or perhaps real attributes. Well, that is the language of dress. You are a Christian. The language you should be putting out is that we must be chaste and moral and upright. You have dignity, and you preach the gospel, witness to the gospel. Yet your dress is saying, ‘I am half lascivious. I like to show off and be an exhibitionist. I don’t care if this is alluring in the wrong sense to womenfolk. This is how I want to deport and display myself.’
The same is true of the women. Christian women should not wear very short skirts and tights to show off their shape, to project themselves. The worldling does that to stimulate sexual desire and to excite menfolk. Yes, you can argue: they shouldn’t be excited, and that is right, but they so often are. That is the wickedness of human beings. And many worldly women dress in order to achieve that, and to put themselves across. That is their dress code. If somebody sees you dressed like that, the worldling thinks, ‘O that is a woman, that is a young woman who wishes to exhibit herself, and to excite others.’ That is not what you want to say, but that is the language of your dress.
These are the things that are important to us, and all the apostle says about the veil to the ancient Corinthian ladies applies to us throughout our manner of dress. You cannot dress in a way that is contrary to the things you stand for. There should be no lawlessness in dress; no provocative dress; no sensual dress; no proud, boastful dress; no expensive dress – ‘I am so special’ – and equally, no slovenliness; no immodesty. It is not necessary that every man who comes to church wears a suit, but what you wear should be respectable and clean and tidy, and not slovenly. We are in the service to worship God, and so we come appropriately, in clothing which is not disreputable, slovenly, or dirty. Women not veiled, unless social custom requires it, but not presenting themselves immodestly or in a way that would deny submission to husbands according to God’s order.