The Great Filter is not likely an astroid or gamma ray burst type phenomena but rather the nature of intelligence that evolves in a competitive environment via evolution. Having two planets full of hyper competitive, violent social apes just means having two planets plagued by petty infighting. And if one planet is insane enough to nuke itself, what's to say it won't nuke the other?
If humans have a big enough presence on a second planet for there to be wars, we’ve almost certainly spread throughout the rest of the solar system and potentially have even put generation ships en route to other star systems, so even if earth and mars are nuking each other humanity will persist.
That scenario is somewhat unlikely anyway simply because access to resources is so much greater at that point, with there being thousands of times more of anything we have on earth in the asteroid belt and other parts of the solar system.
When supply is short enough to warrant it and control is a realistic possibility, sure. Even if humans mastered spacefaring tomorrow neither would be true for many centuries. The scales involved are utterly unfathomable.
The wars we've seen most recently have nothing to do with limited resources. Most wars through history have been about ego/ambition of royal assholes, and hatred/religious differences. Neither world war was about limited resources.
>"Most wars are not fought for reasons of security or material interests, but instead reflect a nation’s ‘spirit’"
While it is possible future wars might be fought over limited resources, that hasn't really been the main factor in most wars that we know of dating back at least 1000 years.
Interesting. Something like 'spirit' is tough to define. WWII could be categorized as a nation's spirit and revenge, but would Hitler had been able to whip up the nationalism required if Germany had been overflowing with resources and was prosperous?
Germany had plenty of resources to assault most of Europe. The resources they did have could have been used for good, but they chose to exterminate millions, and then tried to hide the evidence. They attacked every country around them because of twisted ambition and their corrupt fascist ideology. They were most certainly not correct in suggesting that it was the Jews and gays and everyone they didn't like that was the cause of any problems within Germany. They demonized "the other" to gain support for making war.