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Is it a thing that we should worry about?
Well it kind of depends on whether it's actually happening, doesn't it? :|
Climate change itself isn't something to worry about, as it's a natural process. The problem is that the term is currently a euphemism or a weak phrase for the greatly accelerated climate change that's happening, most probably due to anthropogenic factors. A better term is climate chaos, which I believe has already manifested itself in increased weather instability and greater extremes. Needless to say, as we live in a fairly stable environment here, it probably seems premature to us, but people elsewhere, such as in the Caribbean, are not so lucky.
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If by 'climate change' you mean anthropogenic climate change then yes, very much so. It has already cost lives and livlihoods, typically in parts of the world least able to cope. And things will get worse before they get better - see IPCC 5th Assessment of impacts on human health
https://www.ipcc.ch/pdf/assessment-report/ar5/wg2/WGIIAR5-Chap11_FINAL.pdf
Is it a thing that we should worry about?