Christians not sending their kids to a fight for morally corrupted Rome is a symptom, not a root cause.
The not sending their kids to fight is a secondary (or even much smaller) effect of the impact of Christianity on Rome. Christianity’s social impact as a response to the decadence and perversion of Roman society was broader and deeper - and the collapse of the Roman military was also broader than Christians opting out. (though we are about to see the same impact here with the once-vaunted American military). Christianity as an exploding movement had a huge impact on tipping Rome over…as did overall Roman decadence and social perversion did over many centuries from the fall of the original Republic…and homosexuality played a major role in fostering that decadence.