One of the most effective political action efforts on Facebook, in my humble opinion, is "Repeal the Second Amendment."
Most of the time, it posts a very factual local news report on an accidental shooting, an attempted or successful suicide, or a murder, often by children. Each incident is reported separately with only minimal commentary. But, what it does is turn statistics, that engage your rational mind but doesn't require a personal commitment, into very human stories with emotional power that understatedly provides a call for action and a sense of urgency. And, because these tragedies take place almost every day someplace in America, sometimes several times a day, the cumulative effect is huge.
Also, it doesn't equivocate. While it makes occasional posts about particular legislative efforts related to gun control legislation, it doesn't focus on the minutia of the legislative process or spend a lot of time whining about the undo political power of National Rifle Association lobbyists.
Instead, it sets out, in its title, at the top of every post, a simple agenda. Repeal the Second Amendment. It makes the case that a right to bear arms is bad policy that shouldn't be a constitutional right (which is the case in every other country in the world, even those that once had one in emulations of the United States) on the merits, rather than arguing the meaning of the amendment's ambiguous phrasing.
The campaign is a long haul, movement politics effort to shift public opinion. Everybody knows that the votes aren't there in Congress or in statehouses to achieve its goal any time soon. But, by relentlessly humanizing the consequences of the status quo, it takes on the difficult but worthy task of changing that reality.
It may take many years or decades, but I think that its campaign, over time, is going to change public opinion about the harms associated with widespread gun ownership, and when that shift becomes great enough, change will happen.