Personally, I think only a subset of white people are well suited to red hair, and going by their choices it would seem that filmmakers tend to agree. Redheads (or blondes) who are racebent tend to either not have the hair color or have it toned down. Starfire on the Titans show had pinkish-red hair, and in my experience pink hair suits black women specifically (look at Zendaya in The Greatest Showman). Black Canary in Birds of Prey is really more light brown instead of blonde. Or consider Melissa Benoist as Supergirl. She's white (obviously), but she isn't that suited to being blonde, so they gave her a darker blonde that complemented her better rather than recreate the brighter blonde of the comics.
Now whether this makes any difference depends on who you ask. I don't care in Jim Gordon's case, and I'm not even terribly concerned with Barbara, although if it was all the same I'd have her be a white redhead. I'm just saying that while you might like them to stick it to the critics, it's more likely that they cast Wright because they didn't care about the hair color in the first place. While you'll often hear fans say that they don't care about race as long as the character has the hair color, I don't think most filmmakers make that distinction at all. They racebend because they consider the character's look flexible.
