I used to think it was no big deal that my postdoc research on climate at Princeton was funded by BP, but now I see it as BP's effort to burnish its reputation and influence research.
On balance, taking fossil fuel funding is a net negative and this kind of research should be government funded.
And it's not just oil trying to greenwash. A huge amount of Caltech's new sustainability research is funded by a giant donation from the Resnick family, who gained (and are still gaining) their wealth from growing water-intensive crops in areas that can't sustain them.