The thing is that everyone alive today and in the future is footing the bill for that indifference. It's nice that you don't care, but it's not something I'd brag about.
If you truly care about the planet, don't have children.
At the very least don't brag about not giving a crap.
That's a fallacy; people care about the planet precisely because of children. I don't care about the planet for its own sake; I care because of the humans who inhabit it and their future lives.
Also, humanity spent 100,000 years without flying around the globe, and I doubt they were all living hermit martyr lives.
The fact that I happen to care about other things more than this specific flavor of global catastrophe is morally OK.
Shame is not necessary, but callous indifference is not acceptable. There is a middle ground where you treat it like a habit to improve, like a step count.