I don't agree to the slightest that racism has a central part of Amarrian religion: It certainly has that in their culture, but even slavery doesn't stop at the racial borders. One should make the mistake here and confuse consequence and cause. It doesn't seem to me that Amarrians are racist because of their religion, but rather that they use their religion in racist ways, because they're racists. Anyway, racism isn't reslly the big theme of the Amarr, I think. People just make it so because they fancy playing along the lines of the Third Reich.
Also, even in the middle ages within the Christian clerus itself while you were staying in the church state, there was room to maneuver in/around different questions. In their terms the sacredness of flesh would be a doctrine, while the resulting ban of cloning would 'merely' be a church rule. Giving you room with the latter. And this is especially true if your had some weird cults, there.
And as this is about such a weird cult, I think that Kaleigh has some room to maneuver. If she'd want to play along the lines of traditional Amarrian orthodoxy, there'd be no need for a cult in the first place.
And while the background doesn't say much about the religiosity in the Khanid Empire, I think it had been stated somewhere that Khanid didn't accept the TC's authority to be greater than his in religious questions. I think that implies a similar situation as with the English crown and the catholic church: English king doesn't accept the papal authority - result wasn't that you suddenly had a bunch of pagans and atheists in the British kingdom, but the Anglican church, with the King of England as the (formal) head of it.