Yes. I've told my wife. And most of my friends. I figure if they can't handle knowing that about me, then we weren't as good of friends as I thought. Then again, I have a lot of practice admitting things, considering I also have DID, and that's even more stigmatized/misunderstood.
So yes, I admit to people that I have avoidant personality disorder. Most people, I think, just don't know what it is, and that's easy enough to remedy.