When i lived in a college town, there was a serial rapist/assaulter in the area. They put all these posters up with police sketches from the victims. White dude, average height, average build, dark eyes, dark hair, goatee and a shaved head. I happened to shave my head at the time and had a goatee, so I looked uncomfortably similar to the pictures. At first, my friends starting goofing on me about it.
But, it got to the point where I would have people following me out in public, writing down my license plate number, and shadowing me in stores while trying to surreptitiously call the po-po. WHen I noticed people giving me the side-eye, I'd just shrug and say "I know, I look like that guy, but I am not him." I actually went to the police station and registered with them as "not the guy" and gave them all my info.
I grew my hair out after that. I did keep the goatee because, without it, I looked like a fetus.