She identifies as a girl and Killua uses she and her so why not stick to it? I doubt anyone here is a member of the Zoldyck family who knows that she is biologically male. Like I would also be okay with the opposite, use he, him and his. Why switch? It's so confusing.
More consistent is impossible, everything that is needed about this issue is already on the character's page. Alluka is a transvestite (one type of feminine male) and the current configuration of the page is the best way to convey this peculiar characteristic. Furthermore, Killua has lied several times during the series and is too emotionally attached to the issue to be considered trustworthy; Illumi on the other hand is known for telling the truth even when he shouldn't.
Eh? I don't see any switching. it's uniformly she / her all throughout, going by the mind as the determining factor of personality and identity, as opposed to birth body. As it should be, if you ask me :)
Killua isn't too emotionally attached. Alluka goes by she/her pronouns. She prefers to be a girl. She isn't a crossdresser - she's trans. She has a male anatomy but prefers to live as a girl. That isn't what a transvestite is.
As for the more recent comment, no, she is not uniformly referred to as she/her throughout. Her family, as the article says, often refers to her in male pronouns or refer to her as "brother". This is most likely because they just don't accept that she prefers to be a "she".
Oh, and the answer the OP question more - thee article switches, I suppose, because it has not been "canonically" established that Alluka is trans, so they're covering their bases on the idea of this being a continuity inconsistency and also when distinguishing between referring to her male sex and female gender.