In the novel, and the manga actually does differs significantly on that point, Alicia is basically racist, black is evil, and everything Eumelia does, seen through that prism, shows she is dangerous. Then one day Eumelia is put in charge of levelling Alicia and traumatizes her (over the course of one month iirc), ingraining in her that dangerous creatures are uber scary and need to be killed before they kill her. In the end even though they are battling the dark lord together, only the prince can shrug his prejudice enough to not put her at the same level as the dark lord and justify murder with her hair colour.
That's about it, I will not pretend the novel really makes much sense when it comes to character motivations, subtlety or intelligence.
Anyway Alicia and co never considered Eumelia could have that fairy in a bottle protection charm equipped, then they get quashed by the dark lord and good riddance