In Sartorial Eye for the Clerical Guy, Christopher Benson points to the Mosaic law's requirements for dazzlingly beautiful uniforms for priests as a reason for Christian ministers to wear nice clothing today, with an emphasis on the majestic robes of the more liturgical denominations as compared with the three-piece suits of the congregations I grew up in.
In the comments, someone made the argument that Paul doesn't exactly say anything to Timothy, repeating such provisions for New Testament times. I suppose that's true, but it doesn't go far enough, because Paul did discuss vestments at one point:
likewise also that women should adorn themselves in respectable apparel, with modesty and self-control, not with braided hair and gold or pearls or costly attire,but with what is proper for women who profess godliness--with good works.[I Tim 2:9-10]
as did Peter:
Do not let your adorning be external--the braiding of hair and the putting on of gold jewelry, or the clothing you wear-- but let your adorning be the hidden person of the heart with the imperishable beauty of a gentle and quiet spirit, which in God's sight is very precious. [I Pet 3:2-4]
This is of a piece with the holy expanding to all things [edit: see my Scripture and Worship for the biblical theology of worship I'm working with here], as opposed to the holy/common divide of the Mosaic law. If all vestment can be holy, as all food, all containers, all buildings, and all days are now holy, then the principle of wearing clothing to glorify God becomes more about the inner than what it looks like. So a biblical theology that recognizes this isn't going to apply the levitical dress in a way that requires uniforms for the so-called professional ministers (on the ground that they are the replacements for priests at least in the sense of being the ones paid for ministry) or for the ordinary believer (on the principle of equality). It requires recognizing what Rick Warren wears as being just as capable of holiness and glory to God as what N.T. Wright wears.
When I raised this issue in the comments (I actually just lifted my comment verbatim above), Christopher responded:
Thank you for invoking relevant New Testament passages on clothing. Those passages deepen our conversation. I am wrestling with your contention that "the holy/common divide of the Mosaic law" is gone under the New Covenant, so that the holy is expanded to "all things." All things? Holiness can be conceived in different ways. One way is "a condition of being set apart." What is set apart about a minister who wears the same clothing at the pulpit that he wore for the Super Bowl party or neighborhood BBQ? What is set apart about going to a building on Sunday morning that resembles the bar I visited on Friday night or the mall I strolled through on Monday afternoon? Holiness quickly begins to loses its set-apartness and becomes quotidian and pedestrian.
If we think of holiness as being set apart, then it is a little strange to say that all things are holy, since then there would be nothing to be set apart from. But I think what I said is still true (and what follows is repeated from a comment I left in response). I meant that the holy/common divide of seeing the priestly/tabernacle things and the ordinary life things breaks down in the NT. Every day is equally holy, not just special festival days or sabbaths, as Paul says in several places. Every location is holy and suitable for worship rather than just a centralized temple or tabernacle, as Jesus says to the Samaritan woman in John 4. All food is clean, as Jesus declares and Peter and Paul reiterate. There are no special holy silverware items for use in a special holy building (e.g. what some people wrongly call a church) used for special fellowship meals. There are no special seats that have to be used (e.g. pews). Why should we retain the idea that some clothes are special?
That doesn't mean there's no purpose for clothing. We should still be clothed, for example, and it shouldn't be too revealing. But I don't see why a T-shirt, even one with a rip in the sleeve, or a bright Hawaiian shirt pattern should be any less appropriate for worship than a three-piece suit or dress. There's something special about worship that takes place corporately, yes. But it's not as if that's the only time we worship, and the principle that we should care about our appearance should apply as much during the week when we worship with our lives as it does when we happen to be worshiping corporately with other believers.