Anxiety alone does not cause stuttering, or everyone would stutter. But if you do stutter, then anxiety can trigger it. It's a really frustrating thing, I know. Buy there is also something else wrong there mechanically or neurologically. I stutter when I talk to my parents in Russian, which is my native language, but one I am less comfortable in, since I was only 10 years old when I got to the USA. But I have near zero anxiety talking to my parents, since I do not think they judge me. I do not stutter much in English talking to them. Its interesting.