I've been approached with this scenario twice in the past month: once online, and once in person. And at the risk of sounding callous, my short and simple response to this objection is, "So what?"
It is insufficient to protest with a mere reply of, "Yeah, but it's distracting to others." I will admit that my reply is a bit cocky. After a year of study, I am sure that headcovering is for today. I am confident I can provide a solid argument for this position and that the opposing viewpoint is nothing more than a mere expression of one's personal opinion. Therefore, if there is scriptural evidence that God has ordained something, it is insufficient to protest with a mere reply of, "Yeah, but it's distracting to others."
I will also admit that in spite of it being a personal opinion, there is truth to the objection. Headcovering is a distraction to some people, which further warrants my response of, "So what?" In other words, if it distracts you, what are you going to do about it?
Let's be honest. The word "distraction" is more often than not a thin disguise for what is really going on: we feel irritated with a sister in Christ after we've passed judgment on her. In my experience, people who are distracted by headcovering are those who do not think it is for today and as a result are quite annoyed that some women choose to do it. If we are annoyed because of what someone else is doing, the problem is not with the other person. The problem is in our own hearts.
I am sure there are those who are offended by what I'm saying. But let me flip the scenario because I've actually been in this position myself.
You see, there are two men in my church who persistently wear hats during the service. One wears a knit cap and the other wears a newsboy-type cap. It is the most distracting thing in the world to me. I think, "According to scripture, they should not be doing that!" I find myself irritated throughout the service, grumbling against them in my heart: "Ugh! Look at those two! Don't they realize that they are disgracing their head? How on earth can anybody concentrate on the service when they are wearing that?! They are so distracting!"
Now I am confident that according to 1 Corinthians 11, I am right, and they are wrong. But I ask you, who do you think God is more displeased with? These two men who are wearing headgear when they shouldn't be (and most likely oblivious to what they are doing), or this woman who's got a prideful, holier-than-thou attitude about being right?
I think whatever someone is doing or not doing is trumped by our attitudes toward those people. If a man covers and I'm distracted by it, what are my choices? My first option is to approach the man, tell him he's bothering me (as if I am a poor innocent bystander who has suffered a deliberate assault on my ability to concentrate) and ask him to remove his hat. Funny, I never take that option. Maybe it's because deep down, I know that if I am irritated over something that is really none of my business, it is my sin and I have a responsibility to deal with it.
We love to point the finger at others and say, "Oh, Lord, what about this person? This person is distracting me!" but honestly, if I was truly focused on the service I wouldn't be concerned over who is covering or not covering:
Peter, seeing him, said to Jesus, “But Lord, what about this man?”When I find myself annoyed with a man who chooses to wear a hat, I am only left with the second option: I can choose to ask myself, "So what?" I imagine the Lord would ask me something similar: "So what, Jennifer? So if he covered his whole face, what is that to you? You follow Me!"
Jesus said to him, “If I will that he remain till I come, what is that to you? You follow Me.” (John 21:21-22)