I wouldn't say that Christians think the world can (pun intended) go to hell in a handbasket after we die. I feel a responsibility to keep the planet decent for my kids and their kids (someday) and everyone else here. It's selfish to use it up irresponsibly no matter what your religion.
If you want to say it's because of Christianity, then don't forget that the same religion says we are to be trustees of the earth. So it's just as likely that a Christian would care for the planet because that's their responsibility as it would be that they would figure it's all going to be gone someday and so not care.