German soldiers in WWII wore belt buckles which were imprinted with the words, “Gott mit unser,” translated as “God (is) with us”.
No doubt many, if not most, genuinely believed that what they were doing was morally correct, or necessary, or whatever, at least at some point in the war.
Now, you ask:
“What are the moral implications when Christians are fighting on both sides of a war?”
–I believe the moral implications are very complex. Very few people asked or ordered to fight in a war have any real ability to easily say “no!” particularly when civil law – particularly legitimate civi law – may require it. Moreover, I would posit that more combatants - like the Germans in WWII - genuinely believe that they are the morally superior side, even if caused mainly by propaganda.
Critically, when you write, “Im not saying that the Church is wrong, Im just wondering what the reasoning is behind it.”
–Reasoning behind what? The “Church being wrong,” is apples and oranges to your question, which appears to be “how can Christians fight on opposing sides of the same war?” The response is “very easily, since all involved may be able to make compelling cases that they are morally right to do so.” Compelling arguments can likely be made that, for example, i) Argentina was trying to rightfully retake the falklands from the British; ii) the Confederate States were right to defend states’ rights in 1861; iii) etc., on and on. It seems that these arguments are more compelling if you are, respectively, Argentenian in 1982; a confederate in 1861, etc.
“All Christians live in the higher kingdom of Heaven, so how can we fight each other here on earth just because were are from different countries?”
-Because all of us are flawed, and leaders often start wars for unsound, or at least partially unsound reasons. Period.