Id say I'm average looking with a mild stutter and I've had a lot of dates. Like a few people have already said, it's all about being comfortable in your own skin, and more importantly making them feeling comfortable with you having a stutter. Its not a common thing that happens in most people's daily life, so it's understandable that if you make them feel awkward about YOU having a stutter, it's just going to spiral. Tldr most people don't care, but you have to do the work to make them feel comfortable. Until stuttering is a more accepted thing, it's up to us to make things feel natural.