There are, really several misconceptions about the Amarr Empire going around, I think, the most important being:
First, historically speaking there is no deep rooted conflict between the Empire and the Federation. They used to get along, though wearily. The Federation's true opponent is and always was the State and vice versa. That the Empire and the Federation can work together if they want to shows the example of Heideran and Aidonis Elabon.
Second, the Amarr Empire is going around trying to 'Reclaim' everyone by force. That's just not true, the Empire showed actually a quite rational approach: Those you can easily subdue militarily, you do subdue militarily. Those you can't you deal with diplomatically. Even when the Empire discovered the Mimatar it was due to the natural disaster happening to the Matari homeworld that the Empire choose to invade. When they made first contact with the Federation they quickly realized they had someone on an equal footing there and opted for diplomatic solutions. The same with how contact with the State was made. And they only attacked the Jove exactly because they thought they were an easy target.
As such, third, the idea that the Amarr would get into a war with the Republic and the Federation if the State declared neutrality is thus unrealistic: The Empire might very well push for a non-agression pact with the Federation and concentrate on the Republic while the Federation could then enact retributive strikes on the State without fearing that the Empire would intervene. Or some other such thing.
I think there is factually a lot to loose for the State if it abandons it's alliance with the Empire and little to gain. One has to do a cost/benefit calculation there: And as there are sure benefits, the costs prevail in sum. IOt's all nice and good if one only lists the benefits, but forgets about the costs. If one calculates the costs as well, then one will come to the conclusion that the best option for State and Empire is to kept that alliance up and to support one another against their enemies.
Does that mean that the State and the Empire are best friends? No, of course not. It means the two are bound to one another exactly because they serve their own interests. That this doesn't entirely preclude the State from doing some business with the Republic comes with no surprise: Even the Empire itself is conducting business within the Republic's borders.
P.S.: Shaalira's argument is quite important. One would expect that if CCP puts those limitations of a 2v2 scenario on the game it will also show in the background. Indeed, I think, CCP worked on the background of the 4 factions to put them in sucha situation that the 2v2 situation arises. Now one could say that this is 'just due to game design constraints', but I don't think our chars would say: "Oh no, that historical event that bound State and Empire together was purely out of game design reasons, it doesn't count!"