How can he stay out of politics, in that case?
The Republican Party aggressively opposes any climate change policy, from research to reduction to mitigation. They aggressively support the fossil fuel industry. The Koch brothers, whose combined wealth is on Gates' scale, spend billions to advocate similar positions. The Fox media network, from Fox News to the Wall Street Journal, push propaganda supporting these positions. (These statements are not partisan simply because one party looks bad. Much of it is factual -- clearly that's the GOP's position -- and if you accept the science of climate change, I think their claims clearly fall within the realm of propaganda.)
There is no media outlet that pushes back or calls any of the above on their propaganda, except those too small to matter, and the Democrats are passive.
The best investments Gates could make for climate change might be a political organization and/or a media network. I can guess why he doesn't, but I'd be interested to know. I wonder if he hoped, like many geeks, that he could avoid it and just do good things.