I am not sure it is always possible or helpful to understand why a young child is frightened of someone. I was terrified of my great uncle when I was little because he was so ugly.
Found out later that my mother had also been frightened of him when she was little, again because he was ugly. He was the kindest of men and certainly nothing dodgy about him whatsoever, but there is no denying that he would never have won a beauty contest.
Our parents probably suspected this, but even if it had been widely discussed, it would hardly have been of much assistance- the poor man couldn't help his face.
What helped me, I think, was the unstated knowledge that you are allowed your feelings but you need to control your behaviour.
Screaming and running away when you΄re a big girl of 6 and your mum is right beside you is not ok. Talking of her as horrible and saying how she hates her, again not ok. For this part, the dd needs to be told she is not allowed to talk about other people like this.
But again, I think it would be unkind to push her into interacting with the neighbour. Maybe a wave at the most.
When I was young, I was also scared of men with beards and of bald men. No reason at all, I am positive I have never been scared or treated badly by a bald man.