Personally, I think she should have stayed white. After all, it is her striking red hair that makes her who she is. I understand that the woman playing her can wear a wig but it really isn't the same. Disney should just create new black princesses and stories instead of taking original white ones and changing it just to look diverse.
I actually just read some of the book and it states that first she had blue eyes and then later it says "... a pretty little mermaid was standing beneath them, holding out her white hands towards the keel of her ship." So, she was white in the story. You can read it yourself here : (http://hca. gilead. org. il/li_merma. html ) and it's at the end of the second paragraph.