I don't actually get my knowledge of climate change from Extinction Rebellion (which has some pretty unrealistic demands) - I tend rather to rely on stuff that scientific organisations say.
I think you're missing the point. Yes, a nuclear war was a huge threat.....
IF it happened, and there was no guarantee it would happen. And I'd argue it was never really very likely to happen because actually the Governments on both sides did have a pretty good sense of self preservation. But the point is, it was never a certainty - so the fact that it didn't happen in the end, and we managed to carry on living just fine without being annihilated in a nuclear war is not a reason to start discounting the threat of something like climate change - which really is guaranteed to happen and to be very severe if we don't seriously start reducing CO2 emissions.
Sorry, but that's equivalent to saying that you're not convinced by decades of careful scientific research and an overwhelming consensus amongst the scientific community. I appreciate that news media is not always reliable and it can therefore be worth being sceptical about what popular mass media says. But the concerns about climate change - and specifically the impact on 'freak weather' really does come from reputable scientific sources.
As an example, look at
this page from the Royal Society - which is definitely not the kind of organisation that is likely to exaggerate stuff, or to publish stuff without doing extensive checking for accuracy first. Map B on that page shows an increased risk of flooding due to climate change that covers most of Northern Europe, including the UK (although the map is on too small a scale to identify specific areas within the UK).