Regarding Amarr and cybernetics: Amarr view cybernetics as a sign of royal divinity. They are literally sculpted onto religious statues in churches.
It's definitely not a matter of 'don't believe in it but do it anyway' like Muslims and alcohol. It's a core component of the faith. Amarr are very pro-cybernetics. They are not an anti-transhuman culture, what they are against is, as Esna said, altering the fundamental God-created being (gene alteration). Augmenting, adding to the existing God-created being through 'exterior' technology like cybernetics though is a well-respected thing.
Also, anything that attacks the free will is less welcome by the faith (TCMCs etc, which are very controversial and banned in more religious territories). They like to augment the mind, not subordinate it.
It's also why Amarrian cybernetics tend to be more overt and obvious, when bio-organic synthetic versions are possible. They don't want to hide them, because having them is something to be respected and even worshipped.
"The Emperor and the Five Heirs can expect to live for at least 500 years. Extensive cyber-implants keep their frail bodies alive, even when their organs begin to fail. These cyber-enhancements date back many millennia, and have become a symbol of royal divinity in the eyes of the Amarrians." - Amarr race article, EVEonline.com
Also, @Silas. It's too late to dump 100% cyberneticization. It's more than just Zainou and Sansha. Dusters are 100% cyberneticized as they are all brain uploaded into a computer database. While the sleeper implant is described as being a bio-implant rather than a cybernetic one, there really isn't a whole lot about them that's human anymore. They're described with terms like "entirely digital existence".