Are you going to be upset if Ursula isn't purple?
I find the familiarity argument weak and selective, tbh. The Little Mermaid wasn't a new character when the cartoon movie came out either. Did the red-head Americanized Ariel screw up your image of Hans Christian Andersen's brown-haired Danish Ariel?
Skin color isn't the same as build or other physical traits that are central to a character. It's not like casting Rapunzel with a bald chick. Lex Luthor was bald for a reason specific to his origin story. Ariel's skin color is not central to her story or her character.
Aside from The Princess and the Frog, black girls have been going to Disney movies for over 80 years to watch stories about white princesses. So now they get an Ariel that looks like them. Good. I wouldn't have any issue with them remaking every Disney movie with black leads.
If you or your white daughters can't relate for some reason, the white cartoon version of Ariel is still available literally everywhere and will probably always be the most popular version.