I'm suggesting that it be a focus in life - if it's one of your core values and you care about it, you'll naturally take the time and energy to work against it.
For example, many people on HN care about privacy and government intrusion. They don't need to be convinced as to why it's important to speak up about the NSA and the US treatment of Edward Snowden. People who care feel it's a personal imperative, so they do something about it.
I personally have the time and the inclination. Because it's something I care about. Maybe you don't care about it, that's your personal feeling, so you won't take the time. But I'm sure that there are other things in your life that you care about, and you do invest time in those things.
It's absolutely fine not to care about every social cause out there. I don't think we can expect everyone to care about everything. Just pick those things which matter most to you and work to do something about them.
As for a movement, there are a few out there that I'm aware of - in particular I am a big fan of the work of Mentors in Violence Prevention (MVP).
