a few things in this thread got my attention. First is the assumption that looking dirty will lead people to think you're homeless.
I think it's very desirable to avoid looking like a bum - homeless people get harassed. However, I think people are a lot more likely to make assumptions based of your bike then they are your person. When the two are presented together, which do you think will draw the eye? I've been treated well while wearing stinking sweatstained cotton(Amazingly no one even seemed to notice....) - and standing near my neat, colorful, clean bike. I've had folks threaten me about being homeless in their town from a truck, while I was wearing my best jersey and shorts. At the time, I had most of my clothing drying out over my panniers and I was sloppily packed.
Now I make sure my gear looks nice when I'm going into areas where homelessness might be a problem, or sore spot for the locals. Otherwise, I just towel off a bit at night so I don't stick to my sleeping bag....
I'm not sure rather I believe that the general view of cycling tourists is anywhere near hobo/hippie. I think we're seen generally seen as a bunch of suburbanite retirees singing on for a group supported tour