To explain:
Byakuren does believe in sharing and equality for all, be they human or yukai, but she also believes in salvation through strict Buddhist standards - bring alcohol to her temple and see what happens.
Shinki "I am the law!" Eiki only sees people in white or black and believes in strict social hierarchies and roles - youkai are to behave as youkai should, regardless of whether they want to or not. Any misdemeanor is punished.
Marisa is an anarchist at heart and does not at all believe in personal property, especially if said property comes in the form of Patchouli's books.
Kanako may be a goddess, but lacks the typical authoritarian streaks associated with the head of a cult - instead, she simply seeks to gain as much power as possible by any means possible (including giving the power of nuclear fusion to the birdbrain).