When oil companies can increase their profit by increasing production, they will increase production. Profit-seeking pushes oil and fossil fuel companies forward. There should be other forces in other directions that slow them down. Social demonstrations are important but as long as there is no mechanism to direct those forces in the opposite direction (that is to economically encourage those companies to turn to other areas to earn profit), there will be little effect.
In some countries, smoking companies should inform smokers about the damage smoking causes (for example by printing images of smokers’ lungs on the box, etc). This also has little effect, but the main idea that smoking companies exert a force against themselves is interesting. This can be used in the fossil fuel context. If the tax those companies pay (until a robust reputation system is developed, taxation seems to be the only solution) is used to fund companies working on green energy and ways to limit fossil fuel consumption, the more profit fossil companies earn, the more fund will be available in the sector operating in the opposite direction. Currently, the tax fossil fuel companies pay might be used in social services etc. but if those taxes are exclusively used in the green industry fossil companies will be running against themselves.
UPDATE 1:
A while ago I wrote that tackling the climate crisis (compensating the damages caused in countries due to climate change, reaching net zero emission, etc.) should be in the form of insurance. Countries willingly invest in defence to protect themselves against possible future threats. Tackling climate change should also be looked at as a type of investment for future protection. Climate change disrupts societies, causes huge displacements and numerous other issues. So a global institution is required that operates as a climate insurance company. It sells insurance, invests and pays compensation and develops mechanisms to minimize possible future damages.