Prudery is not specifically about sexuality but more generally being overly concerned about "manners" and "proper behavior", something Pippi completely disregards.
Yes, that's how it's mostly used today. But here are some dictionary definitions.
OED (I've cut the examples)
> prude, a. and n.
> A. adj. That maintains or affects extreme propriety of speech and behaviour, especially in regard to the relations of the sexes; excessively modest, demure, or prim; prudish: usually applied adversely. Now rare.
[...]
> prude, a. and n.
> (pruːd)[a. mod.F. prude adj. and n., said of a woman in same sense as the Eng. (Molière in Littré), in OF. prude, prode, preude, in a laudatory sense, good, virtuous, modest, respectable; either a back-formation from prudefemme (cf. prudhomme) or a later fem. form of prod, pro, pru: see preux, prow a.]
>prude, a. and n.
> B. n. A woman who maintains or affects excessive modesty or propriety in conduct or speech; one who is of extreme propriety: usually applied adversely with implication of affectation.
[...]
> prude, a. and n.
> Hence ˈprudelike a., of the nature of, or characteristic of, a prude; ˈprudely adv., in the manner of a prude.
[...]
> prude, v.
> intr. To conduct oneself in the manner of a prude; to act prudishly. Hence ˈpruding vbl. n.
Websters Revised (1913):
> Prude \Prude\, n. [F., prudish, originally, discreet, modest;
> shortened from OF. prudefeme, preudefeme, a discreet or excellent woman; OF. preu, prou, excellent, brave + de of + fete woman. See {Prow}, a., {Prowess}.] A woman of affected modesty, reserve, or coyness; one who is overscrupulous or sensitive; one who affects extraordinary prudence in conduct and speech.
Chambers:
> prude /prood/
> noun
> 1. A person of priggish or affected modesty
> 2. Someone who has or pretends to have extreme propriety