I really do not care. If someone was to see me while naked, that would be their problem.
Any other problem that my nakedness may cause is somebody elses problem.
For example, I am naked right now and if that bothered you, that would be your problem.
That would not be my problem, I do not experience embarrassment or shame.
The most important thing I have taken from the hypothetical you have provided is that you percieve public nudity as a problem. Do you have undersized or deformed genitalia? are you a fat pig? does Kage: the cultured sociopath experience the emotions of embarrassment and shame?
I mostly wear clothes from when I was younger. A lot of it's slightly too big for me, since the family thought I was going to keep growing. I used to wear black... a lot... so my old clothes tend to reflect that while my new clothes (mostly) don't. 
I tend to wear T-Shirts with a design on the front (roughly 1/3 of them related to Musical Theater, a few game shirts, some random ones I liked, and otherwise a lot of Threadless), black cargo pants, a basic hoody that says New York on it with tattered sleeves, laceless black shoes that grip my feet even when I do things like kicking, standing on my toes, and jumping around, and occasionally a pair of these. 
I used to wear a brick red hoody and a red version of the same laceless shoes, but then the shoes became too battered and worn to keep wearing, and they discontinued them. Did not enjoy jumping back into mostly black clothing. 
I have a new hoody in the mail that's styled differently than what I'm used to, which is a little exciting. It's rare for me to buy clothes anymore. Even if it's terrible on me, it didn't cost much and I'm sure I could find a use for it in the future.