Bear with me if I'm thinking aloud, but I haven't had net in a few days so I'm sort of jumping back into a conversation that's moved a ways away.
I think a muddied theocratic/feudal government probably works out fairly well. Having a sort of civil authority and religious authority, and weird juxtapositions where those cross, isn't necessarily unfounded in history. Essentially, it was up to various feudal lords how things worked in their fiefdoms. Sometimes, that meant religious authorities became landholders, sometimes the church held their lands as organizations, sometimes church leaders were held as advisers to their feudal counterparts. That might surely be what goes on inside the Amarr Empire.
It might be that certain Holders have different ways of dealing with their clergy. Different branches of the church might have different agendas. The kind of preaching Constantin does probably advances the religion a lot, but isn't as politically important. Which might mean the particular wing of the church Constantin is affiliated with might espouse similar views, but he probably also has detractors above his head that disagree with his mode and method. I think, given the size of Earth and the rather diverse views even members of similar sects have, that the Amarrian church is at least going to have some wiggle room.
I think the real question is what might get a priest in hot water. Constantin's mission and preaching doesn't necessarily do much politically, but he isn't in a very politically important position (given his area). Gaven is probably going to be a LOT more heavily leaning on the political side, given his area and what he does. Those are both going to be extremely different than what an archaologist or theological lawyer might do. In the end, the Amarrian religion is probably like most long-lived religions: a vast machine of disparate parts, some new and some outdated, all clamoring to make themselves most important in the discussion but all having a reasonably similar end goal. Constantin, I don't think, has done anything that's going to get him defrocked yet. He's probably not every senior, traditional priest's favorite, but he's probably not doing anything that gets him in big trouble. Not yet anyway.
So when it comes to interactions between clergy (which is, I suppose, the point of all the behind-the-scenes work we're doing here) is that senior clergy can definitely give orders, but they might not be in the same church. I think, given that Gaven is a cardinal (and going by the model I've been using, I'd say that makes him an extremely senior authority), Constantin has to give him a lot of public respect, but they're probably like an Army Colonel talking to an EPA representative. Both might work for the same broad authority, but given their distinctly different jobs, they sort of trust the central authority to reign them in if they go over their bounds.
I am doing my best to make my character not completely step into the sights of the Theology Council. I've always just assumed that the Theology Council, in some way or another, runs the entire business of religion and so essentially Constantin works for them however indirectly. He's definitely subject to their laws, so if he, say, joins a heretical group or shoots down a few Amarrian ships, he's probably going to get defrocked. As it stands, he's just an official doing his best to evangelize and organize foreign believers, but he's nowhere near the lawmaking or law enforcing end of the government. I wouldn't even necessarily call him a government official, though Gaven's got a good point that they're probably all, in some way or another, government officials.