As a person who stutters, I can definitely relate to this. It is a real shame how much effort we put into our career only for it to seem to take five steps backwards due to something we can't control. And I sympathize with you as someone who worked the customer side in the past it definitely isn't easy, and also I will say companies cannot discriminate you in the hiring process solely because of your stutter. It is against EEOC. While I will say customer success and product management is definitely heavily customer focused, if you can do the job well and make customers happy then who cares if you have a stutter? If you make money and the company makes money a speech impediment should NOT be the deciding factor.