I told a couple of people last year, and it didn't noticeably change the way they treated me. However, my case isn't nearly as bad as some others (in fact, one of the reasons I told them was that I was improving and felt that this might be another step to getting better), and I thought that by telling them, they might understand me a bit more (why I didn't go out much, why I've always been single, why I was avoiding people at work). In one case, I believe it helped me build a more trusting and open relationship with one of my co-workers (she's also a friend, I wouldn't casually say this to anyone) because she understood that I wasn't really aloof and it's not that I didn't like her, it's that I was "afraid" of her.
I've never told my family or best friend (who know lices far away unfortunately), but they all know I have some problems socializing and try to help in their own way. I'm sure if I told them they'd understand though, and would be 100% supportive. In fact, I think my mom would have liked me to get therapy when I was still in college, but she never came out and said it.
When I think back to college (before I knew about SA), there was a female student there that often spoke to me about my being too shy and not going out. She never mentioned SA or anything, but she said I was living in a box, and I really should try to break out of it. Back then, I just wasn't ready to change so I ignored most of her advice, but now I appreciate the fact that she was trying to help me even if we weren't that close.
Frankly, I don't see how telling someone you trust and love can be anything but positive. I see it as a sign that you've accepted the fact that you have a problem and are ready to start making positive changes to overcome it. There is always a chance that people will look at you differently, or that some of your friends will avoid you, but the people who truly love you might already know that something is worrying you and should be happy to help you.