I don't think that this is actually decided yet, and it will definitely be dependent on how soon we respond. There are definitely amounts of CO2 we can blast into the atmsophere that will lead to results we can't stop anymore and survive long term. Will we let it that bad? We hope not.
Heck, even if we ignore CO2 and we kept growing in our energy consumption, we could theoretically end up boiling the oceans in few centuries due to all the waste heat (fusion isn't going to help here, even wind and solar would not).
Practically, it likely can't get that bad - but only because the environment would already be too hostile for us before that. And we'd likely will stop that growth even sooner than that simply because we're not that dumb - however, we might also still be too late, because the changes of the environment are dynamic. The system responds, and it can take decades or centuries until the new "equilibrium" is reached, and that equilibrium doesn't have to be one that supports human life - or it might, but unfortunately, the stages before already killed them off.
I sometimes worry that by not wanting to sound too alarmist, climate science might actually self-censor itself. Most of our climate action plans are based on the more optimistic or cautious predictions. There is a fear that by going by worst-case scenarios, people will reject the science, especially if some don't happen: But some of the worst-case-scenarios are also so far away that by the time we realize the worst-case scenariosare true, we might be past the point to do something about it. It's not an easy balance to achieve.
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Space Exploration is a lot of fundamental research paired with great engineering challenges. What we can gain from that is always hard to predict. Space - and other planetary bodies - are also unique environments that allow experiments we simply can't pull off on Earth. Low Gravity, No Gravity, vacuum, solar or cosmic radiation. So it will in my opinion always be useful to have both robotic experiments and human experiments in space.
We probably should not count on space travel, exploration or colonization really giving us a home from home - Mars will probably never be a safe haven to escape to from a dying Earth. Mars might be the test-bed of technology that we'll use on Earth, be it to deal with the consequences of climate change or other environmental changes, or make parts of Earth habitable or useable to us in ways they weren't before. Or something completely different we never could forsee, for a problem or technology we didn't think of when we started the mission.
You can always squabble about cost (including opportunity cost), should we spend money on X or on Y. But the thing with fundamental research is that its economical (and also health and social) impacts are hard to quantify before the discoveries are made and put to use. And when it comes to opportunity cost, one also has to check if there actually is still an "opportunity" to spend your money better. I would say if you already own all the shares for Investment X, you can't do much to get more, so you might need to take Investment Y instead, which might have a lower ROI, but unless it's negative ROI, still better than just sitting on your money.
Might save a lot in traumatic brain injuries while you're at it!
