Alternatively, there has been a nuclear war, and among the mutations are odd-colored hair.
Alternatively, Alice is an Alien.
Alternatively, it is the result of a mishap with chemicals, a science experiment, or some other accident.
Alternatively, a magical setting where magic has altered the human race's genetic structure to where they can be born with bizarre hair colors without any negative effects.
Alice is just a hologram.
In a fantasy setting where everything is brightly colored, Alice's hair is dull brown.
Alice's hair color is rather mundane... Her hairstyle, however...
Subverted: Alice's bright pink hair turns out to be a wig she's wearing at the time.
Double Subverted: ...And then her real hair turns out to be bright green.
Parodied: In a strictly realistically drawn anime, the shounen anime fanboy is drawn in the style of a Shounen Jump hero, complete with ludicrous hair.
Alice's hair seems to change color every other episode. Sometimes it's green, now it's brown, now blue...
Alternately, Alice has bright red hair, which is, in-universe, an uncommon and generally discriminated against color, and she bleaches it to become a blonde. However, her hair turns bright pink instead, and Alice's panic is implied to be that the unnatural pink hair will bring her even more flak...but then the audience finds out that pink is a perfectly normal colour in their universe, and Alice simply doesn't like the color pink. So she just gives up on the natural hair colors and uses a ridiculously (both in-universe and out) deep bright blue dye for the rest of the series...And nobody takes notice of it afterward, even people meeting Alice for the first time.
Alice is a literal redhead. But most people aren't sure whether or not red is a natural hair color.
Averted: Alice's hair is a perfectly normal color.
Enforced: "We need to make Princess Alice more appealing to the young female audience! ... Girls like pink, so let's give her pink hair!"
Lampshaded: "My hair's better than yours, it's improbable pink."
Invoked: Alice dyes her brown hair pink because she thinks it looks cooler that way.
Defied: Alice is faced with the possibility of dyeing her hair pink, but firmly believes that it's too weird of a color and keeps it brown.
"Are you sure pink is your natural color? How does that even work?" "Dunno, but I like it this way."
Conversed: "Dying your hair? Fine, but keep it brown or blond or black, not pink or blue like some weird anime character!"
Alice is mocked for her ridiculously colored hair, and rejected from society because of it.
Alice has fried her hair from dying it so much.
Alice's hair is naturally bright pink, but she dyes it brown and lives a normal life despite it.
Alternatively, Alice's hair is naturally bright pink and most people mock and discriminate against her because of how weird and unstylish it is (sometimes even breaking the Generic Cuteness rule). But like a Big Beautiful Woman learns to use her weight and be beautiful because of it, Alice learns to style her pink hair and look more normal/beautiful/what not. People stop mocking her, or she finds plenty of people who tell her her hair looks awesome.
Alice lives in a universe where a good number of people have odd hair colors, so her pink hair isn't seen as anything unusual.