Absolutely, positively, dress in a professional manner for your workplace, at "one level higher" than your current position. As in, dress for the job you want, not the job you have. Unless you are in some kind of creative artist profession, DO NOT challenge the status quo and wear what you want, just so you're not conforming to "the man's" ideals or expectations.
In a word, it WILL hurt you to dress shabbily or less than expected, and WILL set back your goals of FI unless you have some other master plan for becoming wealthy. On the other hand, looking more professional and put together than your peers (but not ostentatious) will help you excel, whether or not it is right or wrong for society to behave that way.
I'm a manager, and I do not see an employee choosing to dress down as a sign of moxy or independence that I want to promote. I see it as disrespect and/or laziness. Most managers will almost certainly agree.
As others have pointed out, this can all be done inexpensively. Marshall's, Ross, TJ Maxx, Filene's, sales at Macy's, are all your friend. I work in a professional environment, and probably spend no more than $150/year on clothing and shoes, on average. Maybe slightly higher if I need a new suit every couple of years as styles change. Check out a GQ or Esquire magazine at your library, choose a professional look from there, then go buy it inexpensively at inexpensive stores.