Character Analysis
The first description of Idabel Thompkins tells you almost everything you need to know:
It was a girl with fiery dutchboy hair. She was about his height, and wore a pair of brown shorts and a yellow polo shirt. She was prancing back and forth in front of the tall, curious old house, thumbing her nose at the barber and twisting her face into evil shapes. (1.1.66)
Say what you will about the fiery redhead trope being overdone; Idabel embodies it.
Looks Aren't Everything
Besides being redheaded, a big part of Idabel's look is that she doesn't look like people in town think girls should. The barber's wife says she "always knew she was a freak, no ma'am, never saw that Idabel Thompkins in a dress yet" (1.1.67). Miss Roberta kicks her out of her shop, telling her, "don't come back till you put on some decent female clothes" (1.1.97). Even Idabel's sister says, "It don't pay to treat Idabel like she was a human being." (1.1.125).
So what gives? Who cares if she wears shorts instead of a dress? Is that seriously a reason to treat someone like they're not even human? Well, Shmoop, of course, says no way, José, but the people of Noon City might not be as progressive as 21st-century study guides would like. The point is that Idabel doesn't act like everyone else, so she's threatening and suspicious.
I Don't Enjoy Being a Girl
All this complaining about Idabel's way of dressing is another way of getting at the way she is. By refusing to dress like a girl, Idabel isn't just choosing comfort over fashion; she's breaking strict gender rules that say boys and girls must act different ways. And in a society where boys have more freedom than girls, Idabel would much rather not act like a girl's supposed to.
This is best exemplified in the scene at the creek, where Joel and Idabel go fishing and then take a quick scrub. When Joel is embarrassed to strip in front of a girl, Idabel sets him straight:
"Son," she said, and spit between her fingers, "what you've got in your britches is no news to me, and no concern of mine: hell, I've fooled around with nobody but boys since first grade. I never think I'm like a girl; you've got to remember that, or we can't never be friends. […] I want so much to be a boy: I would be a sailor, I would…" the quality of her futility was touching. (2.7.37)
Idabel knows she can trust Joel to treat her like a boy, so she gives him the chance to be her friend. This is a big step for someone as prickly as she is. Only the narrator's comment that her wish is futile shows that the rest of the world isn't as accepting.