It's like going to the gladiator pits to fight because someone was robbed and shot on the next street yesterday and you don't think your street is safe enough.
If we're nuking each other on Earth, I find it unlikely we wouldn't aim a nuke or two at that group's colony on Mars.
The only thing a Martian colony is a hedge against is ecological collapse on Earth. Because we did something exceptionally stupid accidentally. Or because a rock came by to say hi.
Even then, Mars is colder than the Antarctic, drier than the Sahara, has lower air pressure than the top of Mount Everest, has soil poisoned like a superfund cleanup site, has no meaningful ozone layer, has no magnetosphere protecting against CMEs, has half our solar irradiance level, and occasionally has planet-spanning dust storms, so the bare minimum for colonising Mars must be able to survive worse than any possible thing we can possibly do to Earth and also some of the bigger rocks coming by to say hi.
Wouldn't it be far easier and much more useful to colonize the ocean floor than other planets? It is, after all, 70% of the surface area that just sits there.