No, neither factual belief in climate change (in general, or more specifically anthropogenic climate change) nor ideological belief in environmentalism is eschatology ("the part of theology concerned with death, judgment, and the final destiny of the soul and of humankind") to start with, and even if they have a weak correlation with atheism, there is no essential connection between them and atheism (they may sometimes have a common cause, in that both atheism and factual belief in climate change can be grounded in scientific rationalism.)
> And they do proselytize quite a bit.
Proselytizing atheists are disproportionately visible, because people that aren't trying to shove their beliefs down your throat are a lot less noticeable. So, sure, if you aren't an atheists, the people whose atheism you notice will be very disproportionately those who are proselytizers. That doesn't mean atheists in general are proseltyizers, and atheism has no unifying belief in the value of proselytization the way, say, mainstream Christianity does.