I think what these two (the head priest and head of "Babylon") really need is a mediator.
The priest mentioned the refugees earning respect and autonomy and the spymaster thinks they need allies with money and political influence, which aren't opposed goals in and of themselves. Their main contention seems to be the time taken achieving those things. Both of them are right about a lot of stuff, and they would both be better off working together to figure out how to make things happen than at odds with one another, which is hopefully the direction things will go as the relationships between our protags and secondary protags develop.