I've read/watched both Trinity Blood and Chrno Crusade... not many series come to mind with that particular association, but
Immortal Rain might be a little like what you're looking for, but the association isn't as strong. The main character sometimes dresses up as a priest, since, in his past, he and the person who is now his enemy were in a Catholic church-run orphanage and had studied to become priests.
I haven't read more than a few chapters, so this might be way off the mark, but
07 Ghost also seems to have some religious references (with the organization the main character ands up getting entangled with reminds me a bit of the one in Trinity Blood) but, again, having not read the entire manga, I can't really be positive.
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