Molthune is a militaristic country; this reached the point that they have created a specific class for the warpriest with their name on it that specializes in the war domain.
But what kind of gods are specifically advertised in Molthune, much legal? Gorum’s chaotic neutral alignment may clash with Molthune’s lawful neutrality. Urgathoa might cause an undead uprising and create a second Geb. Even lawful war deities such as Ragathiel and Moloch could aggravate the southern countries of Nidal and Cheliax, either by siding with celestial enemies or allowing infernal spies to pass into the country indiscriminately.
So what kind of war deities would be allowed a temple within Molthune? Would fiendishly and/or celestially inclined deities be barred from the country? If so, on what grounds?
Well, said archetype is about focusing on "the militant aspects of their gods," and it specifically allows you to take the War blessing even if it's not usually a domain granted by your deity. So most likely it means taking gods who typically aren't considered "war gods" but have at least some militant aspect to them, and focusing entirely on that. That said:
Iomedae would probably be allowed, and might be one of the more significant ones. She's already pretty warlike, she allows for Lawful Neutral followers, and Cheliax isn't going to get mad about it since they don't outlaw her religion within their own borders (Nidal's opinion on this kind of doesn't matter unless there's actual violence and antagonism, because they ban all religions but Zon-Kuthon's within their borders anyway).
Torag would probably also be one, since he's a good of strategy and defending your own and such. Sure, he's most popular with dwarves, but he's still one of the Core 20.
Martial followers of Irori are usually monks, but it's not like he actually disdains fighting with armor and weapons, and the aesthetic focus on self-mastery might fit in well with the militant virtues of Molthune.
Abadar is all about civilization and he's already got plenty of followers devoted to defending it; since the Molthuni think their civilization is the best, why wouldn't a Molthuni Abadarian want to devote themselves to protecting and expanding it?
And so on.