Several years ago I needed to hire an assistant, selected several applicants to interview and set up the appointments. Since this was an entry level position, most of the applicants were relatively young, either still in college, or just graduated. What amazed me was how the majority of the applicants dressed for their interview: Jeans and t-shirts were the norm for male or female. I think America has fostered a culture which is so focused on ME being ME that young people moving into the workplace are experiencing a shock when this culture doesn't carry over into the workplace.
Honestly, how much common sense is required to know that an interview for a professional position, even if entry level, might require professional attire? This should not be rocket science.
How you dress does make a difference in how you are perceived. It says something about your judgement abilities. It suggests whether or not you are wise enough to handle little things and thus may be able to handle larger things. This kind of perception lies as a subconscious layer in the back of a supervisor's mind and may never get to the surface, but it impacts their decisions AND their evaluation of you, your abilities, and your potential for advancement. Go ahead, say it: "that's not fair!" Do you hear the violins playing? Fair or not, it is reality so get over it.
Give some thought to how you dress in relationship to the position you have AND the position to which you aspire. Dressing appropriately is just one more indicator that you just might be rocket scientist.