Melissa McCarthy as Wonder Woman.  Peter Dinklage as her costume.

When I was a kid, I remember BSing with friends about 'spensive cars.  The name "Maserati" came up.  Later I dreamed of Maseratis.  Since I didn't actually know what one looked like, I dreamed of something like a Ford 4-door sedan with "Maserati" painted on the side in big letters.  <-not really a Maserati.  Form matters.

The reason a character was made white may be as simple as target audience.  Ever notice how most of the characters in Japanese movies are Japanese?  Or while the Legion of Superheroes is largely alien, they look awfully Caucasian?  Target audience.  A more diverse target audience likely requires a more diverse bunch of characters.  But changing an existing character to achieve this is just leveraging the branding.  It's the height of cynicism.  It's not a character, just a product.