For many, this is an old hat.  It seems like worshipers have gone their separate ways on such matters as musical style, use of screens, and Sunday dress.  But for me in my context (where I serve a congregation that worships in both traditional and modern ways), this is a present reality that I have to combat as a pastor who is constantly fighting the “two churches within a church” battle.  So here’s some brief, broad-brush, philosophical/theological reflection on Sunday dress.  (And my saying “broad brush” is a plea for you all not to nail me with your exceptions, as I’m aware that generalizations are met with not a small amount of counter-evidence.  So hear me out.)
#1: Those who defend a “Sunday best” position do so on solid theological ground.  The basic idea is that God is worthy of the best we have to offer…hence our best clothes–ties, dresses, suits, heels, polish, shine, and starch.  “God’s best” in worship is biblical (just think of the luxury of the OT temple and tabernacle, or ponder the implications of the Shema).
#2: (which may come as a surprise) Those who defend casual dress do so on solid theological ground.  Those who hold to #1 often fail to realize that many times (of course not all the time), those who dress casually do so because they value something in particular when it comes to relating to God…and guess what: it’s biblical, too.  It’s a little thing called authenticity.  Perhaps #2-ers are reacting against the down side of years of #1-ness.  That downside is that people can end up in ruts of putting on a show, flashing their best, trying to make themselves look good on Sunday when their home is a mess, their sin is rampant, and their life is in shambles.  Now it’s obvious that #2 also can have down sides–sloppy dress can get into one’s psyche and usher a person into an overly casual approach to Almighty God.
So can #1’s and #2’s never worship under the same roof?  I sure hope not!  Both sides have great reasons, and perhaps the rub between the two is less a matter of good theology vs. bad theology and more of a matter of what one’s upbringing and life’s journey has shaped what their primary values are when it comes to worship and clothing.  The grace-point here for each camp is to acknowledge that the other side has some decent reasons and then apply Paul’s love axiom (1 Corinthians 13) to one situation where it properly belongs.
Jesus, with Thy church abide.
Be her Savior, Lord, and guide,
While on earth her faith is tried.

May she ONE in doctrine be,
ONE in truth and charity,
Winning all to faith in Thee.
We beseech Thee, hear us. 

I’ve been struggling, even within my own church, to encourage Christians that Sunday mornings are not just important, they’re vital.  I don’t know why, but it seems like evangelicals (at least out here in the West) take church attendance lightly.  In Colorado, Yahweh wars with the gods of nature for the attention of the hearts of sinners and saints.  Skiing in the winter…hiking/camping in the summer.  There’s always a reason to “skip church.”  But worship is where we receive the REAL spiritual nourishment of the sacraments.  Worship is where we receive the genuine encouragement from being in fellowship with God’s people.  Worship is where we receive the faithful preaching of the Word.  Worship is where we are SUMMONED BY GOD to be on Sunday mornings (or Saturday if you’re a seventh-dayer).  We don’t question the need for physical nourishment.  Unless we’re fasting or just have out-of-the-ordinary eating habits, we regularly nourish our bodies 3 times a day with food.  God forbid that we Americans forget to eat!  So what about our spiritual nourishment?  If duty is not enough to get us there, maybe our skin-and-bones starving soul will eventually cry out for some self-care.