I think maybe the word "loyal" is being narrowed down to something that's very specific. As an example, I would say that Constantin is a very loyal Amarrian. He is exceptionally devoted to the religion, of course, but also to the government. He still holds the people who ordained him and gave him his mandate in high regard and what he does, he does for what he sees as the greater good of the Empire. In a way, he's up to his eyebrows in his own little Reclaiming, throwing himself passionately into his work.
With that said, not only is Constantin not known for high end pirate hunting or FW, he's also a VERY divisive figure in the church (at least that's how I've played him). He's a multiculturalist who believes that the best way to bring the Word to the cluster is to also learn from them and let people outside the Empire have a hand in reading and translating Scripture. His "diocese" is a loose confederation of believers and churches who he tends to curb the heretical excesses of, but otherwise tends to allow to do whatever they feel is right. That means he sanctions Matari churches that weave Scriptural doctrine into pre-existing tribal customs. He is constantly taking a somewhat left-leaning stance for his people, often bringing up the fallibility of some Holders and often supporting the inclusion of ideas and practices from outside the Empire that seem to work well. For him, it works, though. His ministry seems to be fairly effective and he's well liked even by a fair number of Matari and Gallente.
On that note, the last four attempts on his life weren't in the "dangerous" areas of his diocese, but in the actually dangerous area of the Amarr Empire itself. His ministry divides people not just conservative and liberal, but on a fundamental fault line of whether the Amarr is a race of people defined by birth or a church of people defined by faith. While he doesn't elicit a homicidal rage from anyone but the most insular Holders, he definitely has more Amarrian enemies than not. His most wild supporters are there, too. People either want him made a Metropolitan Bishop or Cardinal, or they want him defrocked and tried for heresy. Part of the reason there's no motion on either front is how deeply controversial he is in the Empire itself.
All in all, though, he's a "loyal" Amarrian by the definition of the word. The situation is just a lot more complicated than that...