No stuttering did not affect my work life one bit, both with customers and coworkers. Don't over think it. I did customer service for 14 years, with over 10 of those years being in a management position and I stutter pretty frequently as well. You will be fine, do not over think it. 99.9% of people do not care about your stutter. You might come across the rare asshole that does, but that is so far and few in-between, you might not even interact with them. Trust me, apply for the job and do not let your stutter deter you. You will enjoy being able to develop the confidence and socialize with other people more. If it makes it easier and less anxious for you, let them know you stutter at the beginning of the interview and that you might pause to answer questions. That is what I do, and it makes me less anxious when I stutter during an interview because they know to expect it. Overall wishing you the best and hopefully this helps!