“What if your girlfriend insists that you wear certain styles of clothing because you are ‘showing her up’? Why does my girlfriend insist that I’m always turned out and color coordinated? If people are going to look down on me because I don’t always wear smart outfits then they are not the sorts of people I wish to impress. My girlfriend says that she loves me no matter what but still gets concerned about how I’ll make her look in front of others. How can I broach this tactfully?”

Tact won't do it....
If she loves you “no matter what” she’ll respect that you are a separate being. While she thinks your clothes are a reflection on her she is apparently devoid of the healthy boundaries necessary to sustain a healthy long-term relationship.