I'll preface this by stating that I'm no subscriber to "corporations only care about profits" school, but:
Do you think this matters to the corporations all that much? You can't "dump" stocks without someone else buying the shares from you. Are these institutional investors going to take a huge hit in the name of climate change? Are the shareholders willing to sacrifice a chunk of their retirement for this cause? I'm skeptical. Where are the alternative investments? The world is awash in capital, with a huge chunk of bonds now paying negative interest rates.
The big risk is government regulation, but we haven't seen a whole lot yet.