How do you get over/ shake off embarrassing moments where you stutter? Or get to the point where it doesn’t bother you?

How do you get over/ shake off embarrassing moments where you stutter? Or get to the point where it doesn’t bother you? I keep being told by my friends and family that when I stutter that it’s not a big deal at all and that no one cares, but to me it fills my head with embarrassment. It’s so hard to constantly feel bad about yourself for these stuttering/ stammering moments and I wanted to hear how you guys don’t let it bother you or have trained yourselves mentally to get over these moments and move forward. Thank you!