I'm going to get into some Shepard Book level of thinking. The Bible has a few words about not killing. Quite Specific... It is, however, a might bit fuzzier on the subject of selling the weapons?
Or to put it a better way, you rob banks because that's where the money is. But you don't rob guns stores cause that's where the guns are.
Every army that is going to march will need two things. The first and most obvious is weapons. Guns. Ammo. Swords. Things that make other things stop being other things. Now, say your sandwiched between the evil empire and the good empire. And the evil Empire is marching for war with the good empire and you're in the way. If you're the guy who is supplying the evil empire with their weapons, they would not dare go through you... that would not only cut them off from your weapons, but also cause the good empire to come to your own aide, because of the kicking the puppy dog aspect.
But, you say, what if the good empire decides you need to be stopped from arming the evil empire... well, if you're arming the good empire as well, they won't have a problem with you because stopping you from selling to both sides cuts them out of their own weapons and gives the edge to the evil empire.
This need not be weapons. Intelligence (your priests are very good at infiltration) or resources (an army marches on its stomach) could be so good and so neutral that either side attacking you would invoke defense from their enemies, who are also getting the same benefits.
This is how both the U.S. and Switzerland managed to be neutral for much of their history (The U.S. until the cold war had basically stopped caring about old war politics and said they wouldn't get involved so long as the Europeans kept their wars over there). The U.S. has historically enforced neutrality by being oceans away and has never been successfully invaded and occupied. In modern times, they are also the largest exporter of military hardware and give their stuff to some rather nasty places because now they are dependent on our spare parts and if that's not enough to keep them in line, the U.S. has all the receipts. It's nice to know how many of your fighter jets the enemy owns.
The Swiss is notoriously surrounded by mountains, making invasions difficult due to the historical need to march. In addition they have carved a niche in both their neutrality making them a great place for hostiles to meet and negotiate safely AND liberal banking laws that have a good deal of accounts from all over the world. You cannot go to war with a bank when they hold your money.
Additionally, although you discounted that option, both nations have a fairly liberal and permissive gun culture. The Swiss Militia drafts all males who are in service from age 18-30 at least and are allowed to take their service weapons home and must keep them in working order and at the ready for recall to active duty.
The United States is far and away the biggest owner of firearms, with private gun ownership in the States representing just under half of all guns owned world wide! There are 105,000 private guns per 100,000 people in the United States, and many gun owners keep their arms ready for rebellion against their own government, so they have no qualms shooting an invasion force.
Both of these attitudes were feared by belligerents. A common joke among the Germans was of a Nazi General meeting a Swiss general and asked him what would happen if I invaded Switzerland with a million men? "Then, I would call all of the Swiss Militia and order them to shoot every single one of your troops." replies the Swiss General.
"And what if I bring two million men?" asks the Nazi.
"Then I will order them to shoot twice," responds the Swiss.
In Japan, Admiral Yamamoto was quite vocal in his opposition to war with the United States and once described an invasion as impossible because the Americans would not sign terms unless he took the White House and "there is a gun behind every blade of grass."