Ilien’s temple holdings are split 4/3 between the IHH and the ETN, as I recall, and the ruler’s heir is a priestess in the “lesser” temple.
Avanil doesn’t enforce a unitary faith on lands subject to it - there are a host of temples in lands recognising (one way or another) the Prince’s authority, including some (e.g. worship of Sera) that might be seen as antipathetic towards the dominance of noble power even though that is part of the remit of Haelyn.
If memory serves, Medoere exists as a separate state as a reaction to the exceptionally (for Cerilia) Papal approach to power favoured by the OIT in Diemed… and within its own territory, the theocracy of Ruornil cohabits amicably with the IHH, doesn’t it?
As I recall, the only state faith in Rjurik lands is that of the White Witch: elsewhere, the worship of Eirik predominates but isn’t required by law, and people are free to follow other deities.
Vosgaard… certainly some of the states have a state pantheon. I’d forgotten about the Vos, I admit. But even there, I don’t remember there being too many state-mandated temples: torva Vos usually permit competition between priesthoods, I think, while the nona Vos even permit other faiths (e.g. Lirovka) to gain real power (i.e. holdings).
For the dwarves - one of the major decisions made by Rich Baker that separates Cerilian religion from that of medieval Europe is that the humans have no creator deity. There’s no god revered as the progenitor of either the world or the human race: all the human deities gained divinity at or after Mount Deismaar, and most were once human themselves. None of them invented any aspect of their portfolio, let alone aspects of the physical world.
But the dwarves (and most other humanoid races) do have surviving creator deities. And the peculiar circumstances of dwarven existence (subject to millennia-old genocide attempts by rival races) makes racial identity especially critical to them. That they have a close relationship with Moradin and his divine offspring is no surprise - but nor is it a guide to human religion, since the relationship between the two races and their pantheons is very different.