Let me put it this way. At what stage does a characters design matter? If we give Superman blonde hair does that change things? Probably not much from a character perspective, but for most people it just doesn't look like Superman anymore. You might be able to argue until you're blue in the face that it's still Clark Kent, that the blonde hair doesn't matter, that nothing changes, and realistically if we were to look at things literally you may very well right. That is real world logic, and if I'm honest I can't argue against that. But we're not talking realism, were talking fiction or more specifically symbolism.
When a character has been defined for several decades or longer with a specific design no amount or compelling argument is going to change people's minds about what the character should look like. We associate the visual identity, his suit, his hair, and yes the skin colour of Superman to the very values he holds, in a similar way that we as a society have done in the past with deities in various religions. This goes for any number of characters and franchises. So returning to this, is her skin colour vital to her characters design? Given Ariel has become one of Disney best known characters for the best part of 30 years, was the film that literally saved Disney animation, and was a character many girls grew up with loving, admiring and cherishing, I'd argue the answer is yes. Does adhering to the design matter? Again from a literal perspective the answer is no. From a perspective of symbolism the answer is yes. What we have to understand is there's actually an important attachment people develop to iconic characters, and to dismiss any criticism of alteration is to not understand why such change is rejected. For some people, it's not just fiction, it's part of a value they hold, part of their upbringing, part of who they are. That's the best way I can explain things.