What is an overview of arguments given by churches that allow women to plait their hair to support that practice? (1 Peter 3:1-6)

If my inference is accurate that you and perhaps the denomination with which you identify disapprove of women plaiting their hair, I'll be upfront in telling you that the passage you quote does not forbid women to plait their hair, wear gold, or dress in finery. To read an apostolic proscription into Peter's words reflects poor exegesis and a faulty hermeneutic. Let me suggest why.

The context of 1 Peter 3:1-6 concerns a marriage in which the husband is a non-Christ follower but the wife is. Naturally, the wife wants her husband to come into the fold of God. What to do? What to do?

In effect, Peter tells the believing wife,

If you want to win your husband over, then model the Christian life for him.

Peter then tells her that she can do this by paying close attention to three aspects of her distinctly feminine personhood:

1. her inner self
2. her unfading, indestructible beauty
3. her meek and quiet spirit

Clearly, Peter is saying that inner beauty is far more important than external beauty.

Ray Stevens wrote and performed a great song back in the 1970s. It was titled "Everything Is Beautiful." Here is an excerpt from that song,

Everything is beautiful
In it's own way
Like a starry summer night
On a snow covered winter's day

And everybody's beautiful
In their own way
Under God's heaven
The world's gonna find a way

There is none so blind
As he who will not see
We must not close our minds
We must let our thoughts be free

For every hour that passes by
You know the world gets a little bit older
It's time to realize that beauty lies
In the eyes of the beholder    

And everybody's beautiful
In their own way
Under God's heaven
The world's gonna find a way

We shouldn't care about the length of his hair
Of the color of his skin
Don't worry about what shows from without
But the love that lives within

I can almost hear St. Peter saying from heaven, "Amen to that, brother!"

That's because true beauty is inside a person; it resides in the "inner man" as the KJV puts it, and not in mere externals. Every person, whether male or female, has that beauty, and it is the gift of a loving heavenly Father. Moreover, I suggest that if beauty is, indeed, in the eye of the beholder, then God our Father is the only "Beholder" who really counts.

The world's notions of beauty change frequently. What is de rigeur one year (or one season, even!) is not de rigeur the next. The Bible's teaching on feminine beauty, on the other hand, neither changes nor is it unpredictable. As Peter points out, in addition to being an inside phenomenon, inner beauty is indestructible and unfading.

That inner beauty is comprised of a meek (or gentle, NET) and quiet (or tranquil, NET) spirit. Significantly, meekness is not weakness; rather, it is strength under control. Neither is tranquility placidity; rather, it is a peaceful disposition, even in the face of persecution and abuse (though Peter is not suggesting that a believing wife should tolerate extreme abuse, whether physical and/or mental, at the hands of her unbelieving husband).

In conclusion, the apostle Peter is not saying that women must not braid their hair, wear gold jewelry, or put on haute couture. Rather, he is saying that if a Christian woman's beauty is merely external and there is no internal counterpart as evidenced in the fruit of the Spirit (see Galatians 5:22-26), then something is wrong with that picture!

On the other hand, if a Christian wife demonstrates through her "conversation" (KJV) or "way of life" (NET) the fruit of Christ's Spirit within her, she may eventually be able to win her husband to the Lord without a word being spoken! Of course, Peter is not suggesting that the husband will not need at some point to hear the message of the gospel and both believe it and receive it, but the Holy Spirit can use a godly wife to bring conviction to the heart of her unbelieving husband. God does the rest!

3:1 Wives, in the same way submit yourselves to your own husbands so that, if any of them do not believe the word, they may be won over without words by the behavior of their wives,

This is one of the most misunderstood lines in the Bible, which in its first glance is a clear expression of misogyny. It isn't. This is to actually teach the women to be creative in their ways to pitch to their husbands the beauty of Jesus' word. Society during Biblical times are truthfully, so limiting to women that any overt attempt for women to Christianize their husband would be seen as emasculating. The women, thus, need to be subtle.

2 when they see the purity and reverence of your lives.

Simply, actions speak louder than words. A naggy woman preaching the Word of God is more off-putting than a quiet woman showing a Christian lifestyle, don't you think?

3 Your beauty should not come from outward adornment, such as elaborate hairstyles and the wearing of gold jewelry or fine clothes.

This is actually feministic, as it says that women, who tend to be insecure about their looks more than men, have to stop validating their appeal from society's unrealistic expectations of beauty, especially men's sexual desires.

4 Rather, it should be that of your inner self, the unfading beauty of a gentle and quiet spirit, which is of great worth in God’s sight.

Again, subtlety and integrity of character as a measure of beauty.

5 For this is the way the holy women of the past who put their hope in God used to adorn themselves. They submitted themselves to their own husbands,

6 like Sarah, who obeyed Abraham and called him her lord. You are her daughters if you do what is right and do not give way to fear.

That again, being lower than a man in the food chain may be an oppressive condition, but it can be used as leverage, especially in showing that the Christian way of life is superior to any other lifestyle.

A smart eagle does not show her claws.