Some surprising opinions in this one. Why shouldn't a security alliance be taking seriously a major phenomenon that has security implications?
Let's remember that we're fat dumb and happy in the west. Food insecurity affects us in the form of food costing a bit more at the grocery store. Because staple foods are commodities, it's a supply and demand thing and as long as we can afford more than other poorer places, we'll get our Cheerios and 5 minute rice. Elsewhere in the world, though, failed harvests due to out-of-pattern flooding, droughts, heatwaves, etc may mean that millions of people don't eat. Millions of hungry people is a major security threat. Wars start and are fought over this. That's relevant for a military alliance.
We'll see increased melting in the north. Should NATO be concerned about a navigable northwest passage? I'd say so. Hell, even within the alliance we've got divergent views (that very much don't work in Canada's favour).
Militaries are increasingly getting pulled to do domestic disaster response for climate-related disasters. This has impacts on force availability and readiness.
Among government departments, agencies, and programs, militaries will for obvious reasons have potentially the largest carbon output. Thinking that governments won't look to militaries to do their bit is unrealistic, and this is a pressure that will be felt to some lesser or greater extent across the major allies. Nothing wrong with exchanging knowledge, innovation, and best practices. The militaries are under civil control, so if the governments decide this is going to be a reality, then the question isn't whether or not militaries will deal with it, but rather, simply 'how?'
So yeah, I get it, this can at first glance be an easy eye roll.. But once we remind ourselves that we have to contend with reality as it is, and that climate change with real impacts on the ground is one of those realities, it makes sense that the alliance should approach this cohesively.