Accepting funding from a climate change denier
It is ultimately up to you. However, if you refuse to collaborate with people who have different political, religious, moral, etc. standards or opinions than you, you'll pretty soon find that you are missing too many exciting opportunities. The disagreement over a climate change is a relatively mild one as far as such things are concerned. You do not need to change your position and you can even try to convince your professor that you are right when you have some chat over a cup of coffee, but I wouldn't take the issue too far. After all, from his perspective, he offers a collaboration to a proponent of some crazy politicized hype and does it first. So I would meet an open hand with an open hand in this case, but, as I said, nobody but you can make the choice.