I'm thinking about this a lot with myself right now. Since I've started seeing someone about stuttering and have started addressing my issues, I've actually noticed a pretty dramatic decrease in social anxiety. I definitely still feel it some times, but that's to be expected after having it for 18+ years (25m here). That being said, I have gone out of my way to calmly introduce myself to more people in the last two weeks than I have in my entire life. Because of that, I feel that my stuttering problems came first and that it then led to social anxiety.