I stutterer but but get emotionally overwhelmed when I hear someone else stutter. How can I desensitize myself?

I stutterer but but get emotionally overwhelmed when I hear someone else stutter. How can I desensitize myself? If anyone should be patient with another's speech impediment, it should be me. But I tried to watch The King's Speech, a documentary on stuttering, and a comic who stutters and I just couldn't do it. It felt too much like second hand shame and embarrassment. Obviously, this reflects my feelings and issues surrounding my stutter, and not anything about stuttering itself. Has anyone else had or is having a hard time hearing others speak disfluently? What did you do? The only thing I can think of off the top of my head is exposure therapy. And yes, I feel like a terrible person since I stutter but have a hard time hearing another person stutter.