My adoptive mother was shy when she was younger although she grew out of it, and I think she taught me "shy" behaviours when she was trying to improve my social skills. That created some problems for me because I'm not naturally shy and I just started believing that my personality was flawed because I wasn't "quiet".
Other than that, no sign of social phobia in my adoptive family, but then few if any of them would have guessed I have it I suspect (although they may wonder why this 33 year old has never shown any sign of having a boyfriend) - maybe some of them have it secretly.
In my genetic family I only know my mother's side, and there is a lot of mental illness and general weirdness, but I'm not sure whether that includes anxiety problems. Probably.
I'm very like them in personality. Amazingly so. When my adoptive mother met my genetic family it was like a lightbulb going on in her brain. "So that's why you are like that, so that is why you do that, or act that way etc". And I just fitted right in with them, in a way I never had before in my life.
But this is not to take anything away from my relationship with my adoptive family, particularly my mother. If I hadn't been adopted I would have been raised by a schizophrenic until I was placed in foster care, just like my younger sisters were. I get really angry if people try and be sympathetic towards me for being adopted. I was the LUCKY one.