It seems clear from the book of James that churches had people that dressed well for church as well as people who could not dress well. Christians are commanded to treat brothers alike, regardless of how they are dressed.
Having said that, it is invalid to take about a "dress code for church" - I don't know of any church that has a dress code to attend. A "dress code" is, for example, that one cannot enter the club without a tie. No one is barred from church because they don't dress like a well-off member or the pastor.
As Christians, everything we do should be to honor and glorify God who saved us... and that includes how we dress.
Because God's word is a book for all time, He doesn't give 21st, or 20th century rules for dress. We have the general principles of apparel throughout the New Testament.
The church (also known as the house of God) is worthy of respect, because God started it and purchased it with the blood of His only begotten Son. I show respect by dressing up for church.
So much of this issue is a heart matter.
Having a set-aside set of clothing for Sunday is a very old tradition... not just a US tradition.