I don't think this is right. Climate change is not known for personally affecting anybody. It's more of an ineffable millenarian idea.
Rather, I would say rich celebrities are obsessed with animal rights, the death penalty, and climate change because those ideas are fashionable among rich celebrities, not because they're relevant to rich celebrities for any fundamental (i.e. would still apply if no one knew what the celebrity believed) reason.
Plenty of educated elites are well aware the problems climate change could cause for them personally. Civil unrest, rising sea levels, and pollution. Things personal wealth only partially mitigates.
Rather, I would say rich celebrities are obsessed with animal rights, the death penalty, and climate change because those ideas are fashionable among rich celebrities, not because they're relevant to rich celebrities for any fundamental (i.e. would still apply if no one knew what the celebrity believed) reason.