Symbolism, Imagery, Allegory
We tend to assign a lot of baggage to people with red hair—you know, like the idea that they're all stubborn, strong-willed, and fiery. Most of it's junk, but there is one thing about red hair that we think is important when it comes to Pippi: it's rare.
Okay, not as rare as it used to be thanks to the cosmetics industry, but it's still pretty uncommon. In fact, according to this Chicago Tribune article only two to four percent of the world's population are natural redheads. So it makes sense that Bengt the bully seizes on Pippi's hair as something to make fun of—"Have you ever seen hair like hers? Red as fire!" (2.56)—and that Tommy and Annika are so riveted when they first see her:
Her hair, the color of a carrot, was braided in two tight braids that stuck straight out. (1.12)
Which brings us to the next unique detail about Pippi's hair: not only is it unique in its color, but it stands out—quite literally—in terms of style, too. Just like Pippi, the hair atop her head refuses to blend in or be tamed, which makes it a symbol of her independence and nonconformity.
That's why it's so important when Pippi combs it out for the coffee party at the Settergrens' house: "For this special occasion she unbraided her pigtails, and her red hair hung like a lion's mane around her" (9.10). This is the one time and place where Pippi is really trying to fit in, and it, uh… doesn't go so well. But does that mean she shouldn't bother trying to fit in? Or that she never will? Or that things may have gone better if she hadn't tried so hard? Or something else entirely? There's a lot to consider here. (And you thought it was just hair.)