The brunettes or blonds in question dye their hair to play redheads, if they can make a black person look like a white redhead without looking incredibly strange due to facial structure then go for it.

The problem. Isn't the actor not looking like the character, it's the character not looking like the character. If the actor for Ariel looked like the character but they made her a reverse mermaid, painted her face black, her hair green, and sea weed tattoos on her limbs I would also have a problem with it.

Though I'm surprised their defense involves people who paint themselves to fit the role considering their opposition to blackface.