Protesting is basically "doing nothing, loudly." It looks virtuous but has almost zero actual affect on policy. Does any politician actually look at a protest and say "Oh, my, look at that, people don't like what I'm doing! Looks like I have to change my mind."
They never change their minds, that's because the police are willing to beat the protesters for them. The Civil Rights movement is an example of (mostly, but not always peaceful) protest that changed things within living memory. Gay rights advances in recent decades definitely owe a lot to demonstrations and public organizing that put the issues into public conversation. Women's suffrage movements also featured many protests. Policy effects are everywhere.
What has no effect pretty much ever is protesting foreign policy, because the majority of people in any country neither care nor know what happens anywhere else.
Civil disobedience and other exertions of citizen power are only a subset of "protest". I've been to a lot of protests and most of them accomplished jack shit.
It's very rare for anything to change as a direct result of protests, but the act of protesting brings issues into the public consciousness that weren't necessarily there before. That is the real driver of change. Changing public opinion directly transforms the Overton Window and limits the acceptable range of opinions and actions politicians can take. Just because no laws were directly changed doesn't mean your protest did nothing.
Politicians are like ROM. You can't change them once they are programmed. If you want a different function, you need to swap them out. Yelling in the street is not going to get you anywhere.
The reason Civil Rights, Gay Rights and so on got traction was not through protestors changing politicians' minds. It was through the masses changing their minds and actually going to the ballot boxes to replace their (essentially robot) politicians.
That's demonstrably false. Politicians like Strom Thurmond and Joe Biden enjoyed long careers in the Senate after opposing the Civil Rights movement. Lindsey Graham opposes gay marriage today.
It was also through the violent actions of terrorist groups that police couldn't keep under control. For every time the politicians agreed with a Rosa Parks, it was because they were afraid of a Black Panthers.
While the police and politicians were afraid, it's not because there was a real terrorist threat from the Black Panthers or other militant black movements of the time. While the Panthers had some issues with violence, almost all of that was dedicated to infighting, and the few incidents that weren't were almost all revealed to be incited and planned by agent provacateurs. They were just afraid of blacks, and of giving the "lower" classes any kind of idea that they could effect change.
