Specifically, protesters who are largely disruptive/destructive achieve two things:
- the do call attention to their cause; it's hard to ignore these morons
- they make me not care about their cause, and hold them in disdain
When someone peacefully protests within the confines of the law, I'm 100% all-in for free speech and open dialogue, even if I disagree with the movement (whatever it may be). But when you decide that your version of "civil disobedience" is somehow more important than another person's right to do something (topic X, Y or Z), then you've crossed the line from civil to criminal behavior. Once you're a criminal, I have little interest in your cause and no time for your shenanigans. I no longer care about what you care about, and in fact, you've turned me into an adversary, if only to counter your arrogant behavior.