Yes it will collapse the civilization, without doubt. It will not kill off the entire species as you said, which is what I am arguing.
Does having a settlement on mars change any of that? Should we not first create self sustaining pods on the earth? After that, what do we need mars for? Just for access to water, sunlight, protection from radiation, and gravity? Surely, a settlement on a big spaceship would be viable too?
It might though. When ice age ended, whole species went extinct (saber-toothed tigers, mammoths etc). Our species somehow clinged on but the population was decimated to couple of hundred individuals at the worst point. Back then we were hunter gatherers so we were much better at surviving out in the wild.
If something like what happened 10,000 years ago happened today, I'm less optimistic about our ability to survive very long. If we were reduced to couple of hundred people back then when we were used to living in the wild, we might go to 0 this time. There are some small tribes of indigenous people in Amazon rain forrest and couple other places who might be better equipped to survive but that is not guaranteed.
I think you are overestimating resilience of our species, we have not yet been tested by any serious cataclysm since modern civilisation, compared to our ancestors, who were much tougher than us though, and they only barely survived.
Does having a settlement on mars change any of that? Should we not first create self sustaining pods on the earth? After that, what do we need mars for? Just for access to water, sunlight, protection from radiation, and gravity? Surely, a settlement on a big spaceship would be viable too?