Perhaps it's different in US, but traveling in Europe I never was hassled by cops cause of my appearance. Happened that security followed me around as soon as I walked in a store, though. lol
And even if cops ran my ID or alike, I didn't mind. I have no criminal record, no open fines and when I was in foreign countries (spend most of the time in UK) I was there legally.
For me, the most important aspect of traveling is freedom. That includes the freedom to wear what I want and don't give a fuck about what other people think about it.
So when I'm on the road, I stand out wearing a hat decorated with these metal things from lighters, a wristband chain made of beer can tabs, my battered fishing vest with padlocks on it and clothes almost falling apart from wear and tear.
Also I find it easier to make money on the streets if you are not mistaken for a backpacking tourist or alike.