War is a sanctioned form of violent crime. It is sanctioned because it is usually inter-tribal, with different tribes having conflicting interests, and sometimes very different, even conflicting laws. Even if laws are not conflicting (e.g. both tribes condemn killing) their laws are usually applicable on their own territory only. So, soldiers invading enemy's territory feel not threatened by any justice system if they maintain connections with their own system standing behind their backs (war supplies) but separate themselves from the enemy's system behind war front. So they can do whatever is not punishable by their own system outside the system jurisdiction: murder of enemy soldiers and civilians, rape, up to a massive racial extermination.
Let's consider an example: how many law systems speculate the prosecution and bringing to the court the act of murder committed by thier citizens on a foreign international soil against indigenous person? Probably not many. The policing organizations of different countries may cooperate to extradite the murderer in some cases but usually the country of origin does not want to "interfere into the internal affairs" of the country where the murder takes place, and the murderer is trialed according to the local law only. If anything, the country of origin is interested in the most lenient option of the local law be applied. It's very similar sentiment to that of treating their own soldiers at war as not criminals but "heroes".
I think you identified properly that "money, religion & land" (more broadly a desire to take away enemy's property and exercise the dominance over enemy) are the causes of war. Religious wars are a form fight for dominance. Missionaries go together with soldiers to "teach pagans the Christian faith" to exercise their spiritual dominance. Process of taking slaves by the warirors is essentially the same, only a bit more brutal.
Your definition of "beliefs" as causes of wars also make sense and probably are present in the invader's minds most of the time. But by themselves, beliefs are not sufficient condition to warrant the war. The desire to take away the property & dominate must be at the core of motivation.