Climate change is one of the greatest threats the human race faces (and is imposing on many other species). And Peterson has made a variety of superficially wise-sounding comments about it which are actually quite ignorant, probably because he's cueing off the sociology of the situation rather than the science.
Some of the science is really well-done, and that alone is plenty to motivate urgent action.
Some of the sociology is really stupid. There's hysteria about this being an existential crisis (not unless summer is an existential crisis!), there's the impression that the world will be destroyed by endless hurricanes and stuff, the glaciers keep being predicted to all disappear way way in advance of when they might actually, and so on. When things get politicized--and climate change certainly has--people have a tendency to get stupid. Especially stupid on the "this isn't happening" side for something which is happening, but it makes the other side stupid, too, because they no longer have anyone to question them hard and make them justify their beliefs (and thereby catch their mistakes), and because it becomes more important to demonstrate tribe loyalty than get the right answer.
So it's not terribly surprising to me that someone like Peterson would see all that and conclude, wrongly, that it's all rubbish and insufficiently understood. I wish he'd go read the IPCC reports on the physical basis of climate change and chase references until he found that, actually, yeah, they know what they're talking about, and gosh, things are bad, and yikes, they look like they'll get worse, and oh did you see just how much heat is being absorbed by the ocean and so on.
However, these dangers are laughably trivial compared to the problems we can cause for ourselves if we fail to adopt values that keep ourselves from fighting each other. In fact, we can't even solve climate change if we abandon Enlightenment values, because it is exactly those values that lead us to the kind of evidence- and rationality-based approach to the world that has given us all the great reseach by the IPCC.
But that's small potatoes compared to the global destruction we can cause with biowarfare, with nuclear weapons, or even with conventional weapons. Even climate change isn't going to cause nearly as much damage directly as we will cause with our migrations and regional wars over migrations and so on. We are frightfully, frightfully powerful as a species now. We simply have to keep it together. If we go insane, we have the power to make things almost arbitrarily bad. (We can't kill all life on the planet. Small comfort, though.)
So although I don't agree with Peterson about very much, I have to admit that if our values get too screwed up, this is a far bigger problem. And with the rise of the illiberal left as well as the long-standing illiberal right, we have cause to be very worried indeed.
(My expertise in social psychology is inadequate to judge for myself whether Peterson is correct about the causes.)