Ugh.. I've been lucky where the people I dated didn't mind my stutter or as my most recent ex put it: "find it low-key cute". I would just talk with her and be firm saying exactly what you said here. Your stutter isn't something you 'fake' and it's actually hurtful that she would say it is. Often Reddit will just instantly tell you to dump someone over one problem which is a bit drastic. Just look at the relationship in the lens of "would I be happy with this person in 5 years" and that should help you.