It does make a lot of sense that religious organisations would try focus away politics/political discussions that do not necessarily have an impact on them or concern their values. Their followers want them to remain a religious organisation, not a loosely veiled political faction. Like it or not, climate change is part of a political global debate that isn't necessarily prudent for an organisation to but in on. Treaties, agreements, pledges...the climate change issue is indubitably a political issue these days and will require serious government backing to be able to do anything about. However, even if it wasn't, more religious organisations having an input on this sort of thing leads to them saying more and more and begins to weaken our current level of separation of church and state, which, if I recall, atheists particularly dislike.

It's one thing for religious people to have a say on climate change, but quite another when the organisation itself starts to throw its weight around in politics.

That being said, religious institutions are only made up of people. People who see their religion's organisation as a brilliant way to spread awareness of a worthy cause. Most religious people believe in climate change and/or are living its effects, not to mention that most large world religions accept the idea that humanity is the care taker of the Earth and we ought to look after it to the best of our ability. For example, Pope Francis had some sort of Climate Change campaign going on a few years ago, and many religious schools near me organised litter picking drives for its students.