I think you should take this as an example how "much" others care about your stuttering. Take it all in and try to change you own beliefs about yourself. If others don't react badly to it, if they wait patiently while you say what you want, why shouldn't you do the same to yourself? Why then should you feel bad for the person who has to stand there and listen to you if he's patient and doesn't show any contempt? Stuttering is partly formed by us getting shamed because how we speak, after a while that shame becomes internalized and we start to shame ourselves despite of what the reality really indicates. To externalize that shame we should realise just how little people care about our stuttering and if you have a grateful situation for that you should use it for your own benefit.