Many of the same researchers that developed the techniques that Exxon relies on to find oil also developed the arguments about anthropogenic climate change. There are certainly individuals within Exxon who acknowledge climate change. I do not envy their cognitive dissonance.
I don't follow US politics very closely, so I don't know whom you are referring to; but if they were a fossil fuel CEO, they may no longer have a financial interest in quitting.
A majority of people in the United States support climate action. Even a majority of self-identified Republicans.