It's not not true though. Climate change is absolutely an existential risk. Maybe it would not be on it's own, but we have nukes. Even a "small" nuclear skirmish could dramatically destabilize all of human economics.

Perhaps the framing needs tweaking. It is inaccurate to say "if we don't fix climate change, it will end humanity". But "unmitigated climate change could spell the end of the world as we know it. Do you like the world as it currently is, or do you wanna roll the dice and risk apocalypse/Mad Max/ etc?" is completely plausible.

Is there a semantic and ontological difference between "er'rybody gonna die!" and "[almost] er'rybody might die!"? Of course. Is there a difference in terms of expectation value of human quality of life in the future? Not a very big one if you ask me.