Hi Gabor,
I used to LOVE acting because whenever I acted, I did not stutter! As Javie said, it is because we are not focusing on our stuttering, but rather focusing on acting. It is the same as using accents.
Firstly, our brain is not used to stuttering while we are acting/using an accent and secondly, we are too busy concentrating on acting/using an accent to stutter.
When I was young, to avoid stuttering, I would use accents when telling my stories, and people would laugh with me because I was being so silly. One thing I can tell you is that people LOVE when we act/play the fool/tell stories in an interesting way because not many people do this. To this day, I am one of the greatest storytellers that I know. I am often accused of being dramatic when telling my stories because I throw myself into my stories, in a way I act out my stories (“play a role”) – I am very dramatic – but it gets people laughing, and I can tell that they cannot wait to hear more!
So do not save acting for the stage, you can “play a role” in your normal life. As Lee says – be a clown, do not take life too seriously!