The thing people are thinking about when deciding not to have children for climate reasons is climate change on a human timescale, not a geological/astronomical one. There is a very real chance that children born today will live through a wildly different climate than their parents did.

As far as evolution goes, there are plenty of species that will not breed or even eat their young when circumstances are not good enough to raise them. It's not that out-there for people to put off or avoid having children due to environmental stressors like climate change. We, as humans, can just rationalize and understand it over a longer time period than, say, a Spotted Hyena.