You don't need to prove anything. Most people who make fun about the stutters are mostly insecure about themselves. You can obviously call out to them if it gets too much toxic for you and see the difference in their behaviour , but overall giving a fuck is time wasted. Instead work on your stuttering for yourself. And yes , it is difficult to make friends and communicate with them if you have stuttering. But i am sure you'll get friends who will listen to you patiently and a partner who'll love you for who you are. So, don't worry and start working on your stutter :).