I used to have this fear, this was the reason why I couldn't approach a random stranger and hit on them.
I was only afraid of what they would think, and still to this day when I approach I become self conscious of how I look, do I look good? How does my t-shirt look, what about my jeans. While I still do it now, in the end I still approach.
Not giving a **** is easier said than done, unfortunately.
When I was much more afraid back then, I would approach, then walk away half way. Like a lame, this was 3 years ago in High School. Think Superbad and McLovin eyeing a girl with a thong then walking the opposite direction when she turns around.