The easy answer would be that Atheists only have one world to live in: this one, whereas Christians believe they are going to a better place later and this one will be destroyed soon anyway so why bother protecting the environment when there are souls to be won!
I suspect the issue runs somewhat deeper though.
Lets have a look at a brief history of Western religion from an intellectual/emotional (head and heart) perspective.
Catholicism was the only option that didn’t involve being set on fire for around 1000 years. It was a solidly established incorporation of Christian and Pagan beliefs and practices, intellectually stimulating for the priests and aristocracy (sometimes a blurry line) and emotionally appealing to the uneducated rabble who didn’t understand the finer points but still got a kick out of hearing a good impassioned tirade in Latin from within the walls of an awe inspiring building. And the liturgy was exciting too.
Then came the reformation, starting in 1517 with Luther and culminated in a divided church and a massive loss of the emotional spiritual with a greater focus in the intellectual “truth” of the teachings of Jesus and (arguably more so) Paul.
As the concept of Science, as an impartial and empirically verifiable means of understanding truth gradually developed, the West saw the beginnings of the rise of the Atheist. Because the focus was or rational truth rather that emotional needs, Atheism had a lot going for it. As science improved the living conditions and colonisation improved individual wealth, the need for a god figure to cry out to when things got tough gradually began to diminish.
Science was better at meeting the population’s intellectual needs than Christianity and it began to become the favoured religion of the educated.
“Secularisation thesis refers to the belief that as societies progress, particularly through modernization and rationalization, religion loses its authority in all aspects of social life and governance.” (Wikipedia)
By the late 20th century, Western Christianity was facing a crisis. The question was no longer “will our children have religion?” but it started to become “Will our religion have children?”
The average age in most major traditional Christian congregations was significantly lower that the average age of the population in total. Christians seemed incapable of keeping their kids in church. It looked like Western Christianity was on its last legs.
Enter the Pentecostal church. By placing the focus on emotional needs, engaging services, interpersonal and theopersonal relationships, and trendy music rather than intellectual stimulation and theological accuracy it saw a resurgence in numbers. In fact, the early Pentecostal church actively discouraged its members from seeking higher education because intellectualism was seen as damaging to faith.
Youth numbers begin to soar. Add the revival crusades and then later the rise of the mega church with sophisticated marketing strategies and emotionally charged worship experiences, and you have mass revival of Christianity. The church which was once the stable rock upon which society was built had to bend and flex to draw in the biggest crowds. The traditional churches are still facing a crisis, but Christianity as a whole seems to have found a way to combat secularisation thesis by appealing to the emotions rather than the intellect.
Now enter the Environmentalist movement.
Technically non-religious or inter-religious, the environmental movement offers many of the things Pentecostalism offers. It is an emotionally charged experience with celebrity preachers who focus more on creating moving imagery than necessarily presenting all sides of the discussion or admitting how difficult it is to predict weather over a week away, let alone over many years. “The debate is over!”
Environmentalism offers everything a religion offers. There are rituals which permeate the lives of the followers. Everything from switching off unneeded lights and shorter showers to spending an extra 30 minutes travelling to work by public transport rather than driving. It even provides and angry god-like “other” which will punish us and our children for our sins if we as a society fail to observe these rituals and religious practices. There are massive rallies and calendar observances, like “Earth Hour”.
Most importantly though, you can be an environmentalist without giving up your other religious affiliations. Pentecostal churches in particular have jumped on board with the environmental movement, giving its members a sense of practical fulfilment in saving God’s creation as well as the spiritual fulfilment from more abstract forms of worship.
Environmentalism appeals to the emotional response. Science appeals to the intellectual response. Physiologically, you no longer have to be “religious” to have a profoundly religious experience which appeals on both levels and which you can share with thousands of others worldwide.
As for why some Christians are not jumping on the band wagon. My observation is that climate change deniers seems to be largely Bible literalists. The literal interpretation seems to have aligned itself in conflict with evolution science specifically and therefore become highly skeptical about the scientific method in general. After hearing evolutionists touting the phrase “the debate is over” about evolution vs creation, it is understandable that the repeated use of the same phrase within climate change discussion is unlikely to illicit a favourable response. They are more likely to examine the case for climate change critically and discard the entire theory if they find any evidence of falsification of evidence by anybody supporting the theory, rather than examining all of the evidence to see if the verifiable observations can be supported. They are more likely to have uninformed disbelief than informed skepticism.
Now, just to be clear, informed skepticism is possible. The science regarding climate change is not exact. The evidence does seem to support climate change being a very real issue, but the only way we will really know for sure is to keep doing what we’ve been doing and watch what happens to the environment. This method may work from an intellectual approach, but it is emotionally unappealing.
So, to summarise:
Atheists are passionate about climate change because it offers a religious experience without having to feel like they are surrendering their intellect.
Most Christians (and other religions) are quite passionate about the issue, promoting responsible stewardship of the planet.
Climate change deniers are mostly Christian fundamentalists who do not trust science to tell them the nature of the world and would rather rely on an ancient book of dubious origin, trusting that Jesus will return before the water reaches our ankles, saving them the trouble of sorting out their recyclables.