The earth isn't going to be hit by an asteroid, it's just going to have more and more catastrophes. If the earth reaches a tipping point with the melting of the polar icecaps, it will still take centuries for them to melt. The tipping point just means that it won't be possible to stop it. Humanity will survive, because killing off humanity would be as difficult as killing off mosquitoes or cockroaches. What will happen, not suddenly in 20 years, but gradually over the next few centuries, is that life will get more and more unpleasant. There will be more famines, more disasters wiping cities off the map. More wars over resources. But, some humans will keep living, and they'll have children, and those children will grow up in a terrible world where survival is a struggle. But, humans will survive, though it might be a very brutal, primitive existence.

As for "capitalism", it's not "capitalism" that's at fault here, it's humanity. It's not like North Korea is a bastion of carbon-neutral utopian living. Humans are unable to think and act on a global scale. They're selfish, and always have been. The difference is that now there are billions of humans, and technology has enabled each selfish human to have a massive climate footprint. Human brains were evolved to exist in small groups on the savanna. The thinking that allowed humans to thrive in that environment has meant destruction now that technology has massively amplified the impact each human now has.

The solution isn't some random change to a different economic system or a different political system. It's either destroying most technology so that each human can no longer have such a massive impact, or it's fundamentally altering the human brain so that people use that technology wisely and with a tiny footprint. Neither of those is likely, so we're almost certainly doomed.