E.C.
K. - my only child, my daughter is 11 months today and she has no anxiety around strangers either! When I leave for work in the morning she does get sad and cry for me, even though she is with her dad all day. But she is over it quickly. Whether with me or her dad, she smiles and flirts with strangers in stores and restaurants. I am scared sometimes that a stranger will pick her up and carry her away without me even knowing, no matter how well I watch her! Actually, at the doctor's office she is the worst, flirting, singing and talking to the doctor while he is trying to talk to us!
I chalk it up to her being very laid back and also being confident that she is loved and I will always be there for her. Ever child is different, as I am sure you have experienced being on your second. Don't be embarrassed...it sounds like you have done a great job showing your son most people are good. Maybe teaching caution instead of fear will be different, but easier to deal with than shyness?
Good luck ;)