An Anglican minister I know wrote:
The goal of divestment is not to cripple these companies economically, which at this point is basically impossible. The goal of divesting from polluters is revoking their social license, to cease giving them the moral cover to keep owning the government through their lobbying, to reposition them as politically toxic, so that politicians treat them more like the tobacco industry (and generally try to avoid being seen in the same room or receiving their money), to cripple their ability to keep setting the rules of the game, in order that more sane rules might be developed.
This strategy has been very effective in the past (e.g. Apartheid South Africa) and is a necessary, though not sufficient step towards opening a space where real climate action can become mainstream.