Was Tsukiko a godless cleric?

[Metastachydium]

Also, on Azure City, I'm also in the "not the capital of the southern continent" camp. There are five nations, AC was just likely the biggest metropolis.

Of course it isn't. Hinjo wouldn't have called the other four nations their presumed allies if it were so (and that's just what we know from the online strips; provided I am not mistaken, there's additional evidence for the same position in Good Deeds as well).
I am aware that my responding to Razade might have been misleading, but I was merely implying it's a ”capital” of sorts for the Church of the Twelve.
Speaking of which…

Several points:

First, by Word Of Giant, the Twelve are worshipped as a pantheon by Southerners of all alignments.

Second, I imagine that it's very rare for a god to cut off one of their clerics, and even more so when it's an entire pantheon that would presumably have to agree on doing it. (Paladins presumably have more explicit rules for when they Fall).

Third, it's possible that "The High Priest of the Twelve Gods" was the High Priest for Azure City, and that other countries might have their own High Priests.

1. Precisely. That's what made me think they have a single, unified church with a single unified clergy.
2. Might be, but when a cleric (of sorts) of a unified pantheon goes rogue and starts killing other clerics of the same pantheon to aid an irreligious guy and the high priest of a god hostile to the pantheon in question who are there to destroy a holy order under the patronage of, again, said pantheon and maybe massacre or enslave a few tens of thousands of their followers… That should perhaps be one of those rare occasions when the idea should perhaps easily get the backing of a comfortable majority.
3. All other high priests we have seen so far (Redcloak and the Northerners) were the high priests of someone rather than somewhere. Naturally, theit might be a number of autocephalous churches dedicated to the Southern gods, but based on what seems to be the norm in the setting, I'd be more inclined to assume that's not the case.