That's false, although I can see how it plays into a comforting narrative that protesters are purists and at best Quixotic, at worst self-absorbed, which makes dismissing them that much easier.
In the real world, any time there's a protest with more than one guy holding a sign, it's a compromise and a search for the intersection of the Venn diagram of the protesters. That's why larger protests tend to become both less coherent (they tend to be unstable and break into their larger and more aggressive subsets) and less strictly logical (differences are papered over by emotional appeals, and of course there is the lowest common denominator effect that the larger the group the more it yields to its louder, dumber members -- or even if it doesn't that's where the cameras go).
It's easy to see these dynamics when it's a protest you agree with. When you think the protesters are wrong, or when they challenge your cherished belief, how much simpler to put them into some prefab intellectual box, close it up, and put it on a shelf. And there are always pundits, either explicitly paid by the status quo or just incidentally benefiting from it, to supply the boxes.