So having a stutter is not common, it is 1% of the population. Also by the looks of the text from OP it appears they likely are one of the stutterers who have social anxiety which is common - I believe the statistic is 60% of stutterers develop social anxiety which obviously makes complete sense and so the best approach for them is cognitive behavioural therapy for social anxiety maybe even in combination with a speech program. Telling them "not to care what other people think" is really silly because socially anxious people (before treatment) care a lot about how people perceive them I know from experience. Also from experience as someone who stutters with social anxiety being told "don't let it affect your life" is also kind of silly because stuttering in combination with social anxiety can really take its toll on how you choose your paths in life. For example many stutterers admit that they didn't take certain positions at a job due to speaking or that they didn't take a higher education for the same reason. For some people who stutter who don't have bad cognitive issues with it, maybe like yourself I presume, it doesn't impede you as much from doing things you want to do. But for some of us it really does and it isn't as simple as "don't care what people think" it is deeper than that.