They feel uncomfortable because they are unfamiliar with stuttering as a disability. I know that scenario well. I always confront people when they mock stuttering by directly asking them either "Are you making fun of stuttering/are you making fun of my disability?". They just need a reality check. More often than not people try to justify that they weren't mocking it and don't even think of apologizing. My most recent example is when I was playing some TTRPG and the DM let a Character say "My name isn't C-C-C-Charles, it's Charles" and I directly told him "Dude, you know I stutter". He went quiet, ignored the issue and continued playing. 2 days later I got a discord message apologizing lol. If people get pissed off that's their problem to be honest, those people can't deal with criticism or don't want to go out of their way not to be assholes.