I just don't really understand the point of the question. I care about "the planet" because I feel empathy for my fellow humans and would like to leave a healthy environment for the future generations to come. I won't leave any offspring. So when I die, my linage ends. After I die I will stop experiencing anything. And yet I still care. But I only care because my brain is wired to feel empathy.

I don't care at all that the universe might have no one to experience it when our sun blows up. As statistically unlikely as that might be.