Apart from the funding and inflation aspect anything that promotes internationalisation may help prevent war. It would be silly for America to have a civil war these days for example, with increasing internationalisation war between countries might also become inconceivable. Bitcoin is an international currency so it may promote internationalisation and reduce war. Maybe
I think you guys have it slightly backwards IMO. You are sort of claiming fiat funds wars which directly causes them. I would claim wars are caused mostly by religion and fiat is pumped out in efforts to get a leg up and produce more weapons/soldiers etc.
So if BTC were to replace everything, they would just pump BTC into the war to fund it.
If we follow your reasoning -- Ideology being the greatest motivator for war; which I will grant for this thought experiment as there is some basis for it(Maslow's hierarchy of needs.), than you have to understand that everyone has unique Ideologies. Any conversation with a person at length will clearly indicates that while they may be herded like sheep for a cause by a demagogue they have their own unique philosophical beliefs as well and selfish motivations. Demagogue's are powerful with the tool of fiat because they can socialize and amortize the costs of war. If Bitcoin is pervasive, demagogue's will have a more difficult time extracting large pools of funds so easily to fund wars because convincing their followers to go along with their specific plan is more difficult when they have to directly fund it.
Sure their may be fractured conflicts of groups of people with different idealogies.. I.E... ALF vegan bitcoin group raising funds to firebomb a Animal research facility, but these will be more tactical and efficient attacks because of their inability to use Fiat to steal the wealth of a whole nation.