Bear in mind of course....
"The Kith'rak is not acting as a Kith'rak should!" - Because I know I'm in the right, of course, and he didn't agree with me, so, naturally he absolutely must be in the wrong! How dare he!
"We're meant to undergo purification!" - Because purification certainly does not mean 'a swift death', of course not... no, they would absolutely bring someone who was potentially about to turn into an illithid to the creches where they raise their young, yes, that makes sense! Never mind that there's no known cure for an illithid tadpole in our society that does not have openly practicing clerics... no, it's a mysterious purification rite, which I am not allowed to know the specifics of until I'm an adult and permitted back into full society; there's no way they'd keep the fact that death is the only cure from those who hadn't completed their rite of passage yet, never!
"Vlaakith would never sanction the death of her own people for the sake of capturing an important relic!" - Vlaakith, the lich queen, who above all else covets power and who has supported a society where inter-clutch murder for the sake of competition and advancement is commonplace. Vlaakith who routinely 'honours' her most successful and high ranking warriors to a special audience where she devours their soul to feed her immortality. No, she'd never!
But it is pretty on brand for your standard githyanki - who generally treat the very idea that they might be wrong about something, or that they, personally, may make mistakes, to be anathema and impossible concepts.
Lae'zel, of course... is most likely some form of special bloodline, or favoured individual - I'd say princess, if Gith society had such, though they generally do not; they *used* to have a royal succession, but Vlaakith (Vlaakith the 157th, that is) refused to select or produce an heir of her own right up until she died... at which time she returned as a lich and kept hold of the crown with a tyrannical death grip ever since. Lae'zel is probably descended of a line that traces back to a clutch of the previous Vlaakith in some fashion, and is the secret heir of her people, the only one with the true right to challenge Vlaakith and claim the throne of the githyanki people for herself.
This is Larian we're talking about, after all.