Liberal groups, meanwhile, have accused conservatives of using #block/report to shut them down.
The battling allegations have led to competing blog posts that offer some of the same advice.
Liberty Chick, a columnist for conservative site Breitbart.com, encouraged users to report suspected abusers, while Charles Johnson of left-leaning blog Little Green Footballs said he would continue to tell his followers "to block and report" those who harass them.
However it's used, Twitter has clearly become a key destination in the national discussion. Twitter said a record 10.3 million tweets were sent during the first presidential debate last week, making it he most tweeted-about event in U.S. politics.
And for people sick of politics poisoning their feeds, there are Facebook pages such as "Nobody Cares About Your Political Posts. Really," where users can vent their frustrations.
The page promises to be "Open to all conservatives, liberals and moderates who are tired of the constant stream of political posts on FB. Doesn't mean that your views are not important -- just means that it isn't important to us to hear you blather on. P.S. You do realize that you really aren't changing anyone's opinion, right?"
It started out as friendly barbs on Facebook, childhood friends sparring over differences in the presidential election.
Sarah Mirocha supported Obama; her friend supported Romney. But by the time the conversation was over, the two were no longer friends -- on social media or otherwise.
"One less hateful troll = more peace on my page," Mirocha, 43, wrote in a Facebook post.
The Iowa-based writer made no apologies: "It's my page, isn't it?"
Yes and no, says etiquette blogger Thomas P. Farley of What Manners Most.
"The beauty of social media is that it does allow us to be commentators on the news. But you have to be aware of your audience," Farley said. "You know these people would never say anything to your face. But it is sort of an unfortunate consequence of anonymity online."
For many people, the hardest part of the 2012 political debate may be restoring friendships that have been damaged.
"I think that for friends, real friends, it will get better," said Stevens, who after the election plans to restore a number of Twitter voices he has muted. "I think for people that are partisan acquaintances, it will probably calm down a little."
But Farley believes repairing friendships damaged by political differences will probably take a little work.
"If it's somebody you see regularly," he said, "I would have the conversation in person."