My brother is ISTP. When I think of the words "socially anxious" I picture fretting, and he doesn't really fret, he just gets annoyed with social stuff. I guess you could call him shy. He is definitely reserved.
It's funny for me to think of him in terms of these words, because he's a total crazy with people who know him. Others who don't know him, though, perceive him as either rude or boring with not much personality. SO funny to me, knowing him as well as I do. There is no lack of personality. He's emotional, hilarious, daring, smart, and adventurous.