That's the problem with colonization as an Earth back-up—even Antarctica and the Sahara Desert are more livable than any other body in the Solar System, by a long shot. Another Snowball Earth or a heavily desertified Earth would still be preferable to Mars. Throw in a fair amount of radiation, even—still better.
Cuts down significantly on the sorts of events for which a Martian back-up world is preferable to a shelter-in-place strategy.
Basically what we witness so far and will keep on seeing are spikes in all directions of the spectrums (e.g. record high temps, but also record lows; rain in the Death Valley and droughts in formerly wet areas). More critically, what little we've been able to gather on how fast climate eras shift from one to the next, it appears that whereas in-cycle change happens rather slowly (change within an era, because averages), climate era shifts could happen very quickly (because chain of events). We're talking going from a warm era to a glacial one within a few years, sometimes months even. A high speculation is that some thongs might upset the Gulfstream and you'd observe climate evolve from year to year.
Still probably higher than extinction from war in the same time frame.
Life on earth could end in the next five minutes. :) https://www.youtube.com/watch?v=RLykC1VN7NY
I don't see the "we must migrate now" types saying "lets put migration away for a while so we can better build anti-asteroid solutions and detection systems."
Arguably, we're just a couple launches and deployments of mass drivers away from fixing this issue. This is all known tech that could be deployed relatively quickly. A self-sustaining Martian colony is probably hundreds of years away considering the work it would take to terraform the planet.
. . . actually I have absolutely no idea how you would practically do that at all.
But I have heard the possibility of a GRB discussed seriously as a motivator for expanding, not just through the solar system, but through the galaxy.
Why not? If a big asteroid is going to hit earth (for example), fleeing is a pretty reasonable response. It's also a reasonable defense against technobiological hazards.
To compare, the Triassic–Jurassic extinction event created an Earth still more liveable than Mars. Even if we go way back in time, to when there was no land-life on Earth and a poorly oxygenated atmosphere, the Earth is still better off than Mars for supporting human life.
If the goal is to save the human race, then it'd be better to have a few high orbit or lunar habitats, then if something wipes out the majority of civilisation on Earth, we immediately begin recolonisation of our home planet.
Because that's basically what this sort of thing comes down to, at the end of it. There's basically nothing that is going to be existentially, immediately threatening to earth on a timescale that Mars is actually a more livable environment.
Where else in the Solar System could we even get the amount of water we would need?