Certainly the protestors sincerely care about the environment and truly believe capitalism is evil. But hardly anyone in the marching throngs has actually seen a sea turtle, nor would they miss it if the species became extinct. And if sweat shops are closed, third world children will starve. The protestors see this logic, but don't respond, even when persuaded that turtles fare fine under existing laws and children benefit best from unfettered trade. Logic doesn't impact because compassion doesn't motivate.
Compassion is only a pretext for self-expression.
Compulsive Self-Expression Disorder explains why the protestors deliberately choose such futile methods of persuasion. Surely they're smart enough to know that though vandalizing mobs can intimidate a city, their tactics merely infuriate a nation. But no one is striving to win arguments. They're trying to get attention. At that, their methods have succeeded brilliantly.