Does anybody feel like stuttering discredits you?

Does anybody feel like stuttering discredits you? I interviewed for a position as a front desk assistant yesterday that requires a lot of people interaction. I have 3 years worth of customer service experience working as a cashier and front office receptionist. I had all the qualifications and trainings required for the position, but everything went down the drain once the interviewer heard me stutter. It’s like all my skills were nullified by my stutter. I don’t have trouble talking to customers, but interviews are something I still struggle with.