Discrimination is real. Some types are worse than others, like how the United States used to enslave people because of the color of their skin.
But hair is a real reason people discriminate nowadays, and although it isn't a reason we turn people into slaves, people do feel the effects of hair discrimination. Let's look at your princess movies and see if you're at fault.
(The Lion King doesn't count, since you can't classify the lion manes or bodies as a distinctive color, and lions have fur, not hair.)
Blonde princesses seem to be the best off when it comes to negativity on their hair color. Cinderella's only fault is that she talks to mice, and even that isn't that bad. She was obedient to those who treated her badly to avoid conflict. Aurora (Briar Rose) is the one best described as beautiful, and she has such a sweet love story with true love waking her up. Rapunzel is the adventurous, super positive girl who escapes from one of the most tricky Disney villains of all time. Elsa (although almost more of a white than a blonde) may be a little misunderstood, but she has power to change the world and isn't pulled aside into marriage like every other princess (except Merida, of course). You've done a fairly well job here, Disney, in proving the stereotypes of blondes wrong and showing that there's more to them than their hair.
Black-haired princesses have it pretty well off as well. Mulan is the inventive girl who rises above stereotypes to save all of China. Jasmine is the girl who chooses her own destiny and goes her own way in how she wants to live. Snow White is the super kind girl who is poisoned by an evil witch, and her story is as beautiful as Aurora's. Pocahontas saves two rival groups from going to war and makes a bond with an English settler that is sincere and peacemaking. Tiana is the girl who never gives up on her dreams and would rather fulfill them than do anything else in the world. I don't really hear much bad news about black-haired people that doesn't have to with their ethnicity and skin color, but you handled those pretty well.
But what about the brunettes? What have you done for people like me? We have Belle, the nerd who falls in love with a beast. Sure she overcame stereotypes, but what does that gain? She didn't save China or show girls the power of females going their own direction. She just chose the lesser of two evils in her love triangle, and even then, her father's debt forced her into love. And how about Rapunzel after her hair gets cut? Her hair lost its magic. Sure, Eugene (Flynn) liked it better, but he's a wanted criminal. And he had to like her blonde hair enough to fall in love with her in the first place. What about brunette stereotypes? We aren't called anything bad, but brunette seems somewhat sub-par. Guys in books and movies who fall in love with blondes love it for being swooshy and beautiful, but the ones who fall in love with brunettes call it mousy and messy and they overall love their brunettes for their insides, not their hair. This doesn't mean that brunettes are horrible people, just that they usually aren't that special. Disney, you haven't done much to change that idea.
And lastly we come to the redheads. Ariel is the discontented girl who gives up her voice because she's sure that Prince Eric will fall in love with her without it. It was a pretty close call. Merida is a wild thing who defies having to marry at all, which isn't all bad, but she does nothing to break the stereotypes. Ana is the impetuous girl who decides to marry a man she had just met that day. Even Elsa, the queen who was maybe slightly crazy at the time from keeping in her fears, told her that it was a bad idea. All this actually somewhat proves the stereotype that redheads are tempered, impetuous girls who may or may not have souls and steal them from other people. I have a sister with red hair, and I don't see these stereotypes as dominant in her more than people with blonde or brunette hair. Disney, what have you done?
Your faithful viewer,
P.S.-I don't actually believe in any of these stereotypes. I'm just calling it like I see it.
P.S.S.- You do have really great movies. If you would just fix these few things, everything would be a little better.