The opposite is true. If you want to credibly assert that fossil fuel consumption at the point of extraction can be controlled by consumer behavior it is you who needs to bring evidence.
Even discounting that boycotts cannot work without accompanying violence.
When the plastics industry, an industry concerned with the mere byproducts of fossil fuel extraction, realized that public opinion was turning against their products, they created a multibillion dollar campaign to convince everyone that those plastics were fine and would be recycled even though the technology was never available or cost effective for large scale use and all that plastic waste was just getting dumped in landfills and shipped across the ocean to foreign landfills.
That misinformation was the accepted wisdom for thirty years.
That’s what the industry concerned with the unavoidable byproducts of extraction and refinement of fossil fuels did when everyone started to turn against them after literal decades of grassroots propaganda around litter.
They gaslit the world into believing that it was okay to use plastics for packaging because they could be recycled.
Even if you still believe that you and all your friends can change the course of the main event, the most powerful wealth extraction industry ever known in human history, and keep from being turned against each other, made into pariahs, expelled from society and keep the points of your own knives aimed away from yourselves simply by deciding not to buy fossil fuels, what do you think they’re gonna do?
They’ll just load em up in a tanker and send em over to a place where someone will.
And sell you plastic doodads that run on electricity that is still made by burning fossil fuels.
I don’t need to provide evidence that we can’t change the path of the extractive industries with boycotts, I’ve spent my whole life living in the outcome of that reality.