I've had a similar situation but they thought I was on drugs. I was able to make a joke along the lines of "I stutter when I'm sober, NOT when I'm on drugs" which is actually true but it made him smile and he was able to see that I did have a natural stutter so he was cool apologized and left me alone. Sometimes you just have to let it happen and not let it bother you. Even make jokes about it to ease everyone's tension who are unaware or even don't know it exists. No one owes you any sympathy or understanding. The most you can ask for is respect, and sometimes that has to be earned. Keep your head up and work on the confidence. It difficult but not impossible.