I've read the book The Princess Diaries, and in that one they simply cut her already straight hair and dye it blonde. I think in the movie, they wanted something that would be very dramatic. The huge curly hair at the beginning was likely a wig, since I believe Anne's hair is naturally straight.
That said, I remember being very annoyed with that, since I was roughly Mia's age when the film came out and had really come to terms with my curls at last.
Connected or not, later that year I got my hair chemically straightened (NEVER again).
What's ironic for the film, though, is that they make two very good points: the first is that they straighten her hair to make her more Princess-like, but Mia fights her "transformation" all the way through. It's made clear that they're kind of trying to make her seem less unique. The other is that the boy she ends up with loved her when her hair was curly, and I think liked her more when she was "just Mia" as opposed to Princess Mia.
So the curls aren't a deterrant for love, and the only person who really finds her "acceptable" afterwards is the jerk.