This has always been my fear, to see someone wearing the same clothes that I am wearing at work or whenever I go outside. However, come to think of it, I think my fear is baseless and there is nothing wrong in seeing someone similar to you in terms of clothing or apparel. It is also unavoidable. The important thing is I feel comfortable in my favorite clothes and enjoying life.
I did not encounter it yet. I just remembered that I watched a movie before, where a manager track trainee was wearing the same exact outfit as what the director of the company was wearing. It was a comedy movie and it ended up to a point that her boss has to terminate her due to multiple instances of having the same clothes.