In regard to your point about CCEF accepting funding from PXP, I have noticed the issue and the wider consequences. One of the long-term effects of nonprofits accepting money from groups like that is that depending on the amount of money and how it is used, the money can create a long-term dependency. I have seen a couple of environmental nonprofits accept money from corporations, then when the corporate purpose is fulfilled (like when the law they wanted gets passed with help of the nonprofit), then they have no need to continue to provide funding. The funding gets pulled, and the rug gets pulled out from under the nonprofit, leading sometimes to devastating consequences.
So, see attached link to Wired, where PXP was able to fund a university researcher, and that researcher wrote favorable studies.