Before I answer, as a quick aside, when one talks about pacifism is paramount in Buddhism its important to clarify that it very specifically speaking about people who take vows and become monks. These vows are only applicable to the monastics who take these vows. You are asking about monastics so the question is totally valid, but I wanted to clear up the popular perception that Buddhism preaches pacifism in general. Its really only people who taken the vows that are not supposed to kill.
So that digression aside. How can these monks justify foresake these vows and participate in killing? The short answer is with mental gymnastics that twists Buddhist teachings towards to their own needs.
To illustrate this point I will look at the Zen priests who cheer-leaded Japan's violent colonialism and aggression during the WWII era. I will leave aside why they cheer-leaded this violence (unless you are curious) and focus on the how they did it.
In short, one of the most popular ways they did this was to simply twist buddhist concepts in a way that meet their intended philosophical target.
The first quote we will look at is from Shaku Soen who is an extremely important Zen master in terms of lineage. In talking generally about war he writes:
And this example should be made the ideal of every faithful Buddhist. Whatever calling he may have chosen in this life, let him be freed from ego-centric thoughts and feelings. Even when going to war for his country’s sake, let him not bear any hatred towards his enemies. . . He may have to deprive his antagonist of the corporeal presence, but let him not think there are atmans, conquering each other. . . The hand that is raised to strike and the eye that is fixed to take aim do not belong to the individual, but are the instruments utilized by a higher principle than transient existence. Therefore, when fighting, fight with might and main, fight with your whole heart, forget your own self in the fight, and be free from all atman thought
Here Shaku Soen is taking Zen concepts such as oneness (emptiness) and no self and twisting to make the point that essentially says "If none of us really exist as separate selves and ultimately we are all one, we aren't doing anything bad".
This type of thinking can be directly tracked back to a medieval Japanese Zen master Takuan who makes similar points:
Stated in terms of your swordsmanship, you should not think about techniques for striking with a sword. Forget all striking techniques and strike. Cut the other person, but do not dwell on the other person. Both self and other are emptiness. The striking sword is also emptiness. But, do not let your mind be restricted by emptiness.
Another way Soen justifies War and Killing is that everyone gets reincarnated anyway:
Many material human bodies may be destroyed, many humane hearts be broken, but from a broader point of view these sacrifices are so many phoenixes consumed in the sacred fire of spirituality, which will rise from the smouldering ashes reanimated, ennobled, and glorified. The spirit which dwelt in them and brought them to the altar now assumes another material expression in the form of coming generations
Jumping backwards in time and looking at the Sohei Monks, the general philosophical justification is basically that a violation of secular law is indirectly a violation of religious law and also they believed they were living in a time of religious decline that necessitated drastic measures. Mikael Adolphson makes the point in his paper "Discourses on Religious Violence in Premodern Japan":
This brings us to the second type of ideological justification, known as the “interdependence between Imperial Law and Buddhist Law” (ōbō buppō sōe).24 The concept first appears in a tenth-century document, which explains that a violation of the Imperial Law was also a crime against the Buddhist Dharma. A more explicit case emphasizing their interdependence emerges in 1053, in an appeal filed by an estate manager from Tōdaiji, where the complainant compares the laws of the state and those of Buddhism to the two wings of a bird and to the two wheels of a cart.25 The interdependence of these spheres was used to justify violence in times of a perceived decline, when Buddhism could be seen as the final line of defense to protect the imperial state.
A point he also makes in the paper is that the monks believed that they had divine justification because the Kami or indigenous nature spirits were on their side since they were "good monks".
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