Personally, I don't know if anxiety can really get in the way of a good relationship.
If people care for one another, can it really be an issue? I could blame my anxiety disorder for the last relationship I was in failing, but I think that if that girl really cared for me, it wouldn't have been important to her. And it was very important, she felt embarrassed with my disorder.
I was in a relationship before in which the girl really cared for me, and I for her, and I never had anxiety when I was with her. She was the safest person in my life, she understood me and my disorder didn't bother her. I think it's the thing I regret most, that I broke up with her. I never understood why I did that I imagine I didn't feel I deserved her, somehow.
Lately my disorder is getting to my relationships in a different way. Besides my avoidance behaviour making me miss the situations in which I could meet someone, I'm too messed up inside to allow myself a new relationship, I fear the moment it ends (and am positive it will not only end but end because of my issues), I stopped believing I could meet someone who didn't make my issues a big deal, etc... Don't even know why, simply that I can't see myself with someone anymore. Not that I'm a bad person, but for now I'm too hurt, sad in a way that won't help. But time heals, so I hope I'll change my mind about this soon...
But I still think people should always remain open to relationships. Even if someone's shy and gets embarrassed by talking, who can tell if the other person isn't above those things if they connect? If one allows things to happen, they probably will. It's harder to deal with relationships when you have an anxietydisorder, but so is most of the things, and we do most of it all the same. It's good when we go for it even if we know things will probably don't work, the way I see relationships, even if chances would be so low as 1 to 10 (I think they're better most of the times...) we must get through the 9 "wrong" ones to get to the 1 that counts. And even if one makes a fool out of himself, does it really matter? Isn't the 1 worth the chance?