My opinion is that no change of climate (beyond external impact) would be able to wipe humanity from the face of Earth. Even world-wide nuclear war would merely dent the total human population numbers for a few decades at most.

Food production and logistics are getting more effective and more efficient over time, any hunger that has happened in the past century and will ever happen — was and will be entirely social/political in nature. We’re in no danger of food randomly disappearing naturally, as far as I understand.

We are in danger of social changes though. Current civilizations might collapse, bringing hunger and death to hundreds of millions.

A serious dent in the human population or something as severe as a world-wide nuclear war would look like a complete destabilization of existing supply chains and world economy. Sure, humans might exist on earth but nothing about the quality of that life is guaranteed - might be backed to subsistence agriculture at best and never recover since all the raw materials that are accessible that let us leave that kind of lifestyle have been thoroughly mined.

Basically, the current quality of life is never again attainable by any other species full stop because of those resources having been consumed to get to today. If the point of life is just to exist as animals then sure, no need to worry. If the point of life is to reach and strive to touch the stars and achieve a kind of immortality for our species, it feels like we’re in danger of permanently dooming planet Earth to never producing such a species.