While the justices tend to describe themselves as being apolitical, the court of Chief Justice John Roberts has shown a distinct preference for speech cases that concern conservative ideology, according to an empirical analysis conducted by researchers affiliated with Washington University in St. Louis and the University of Michigan.
The analysis found that the justices on the court appointed by Republican presidents sided with conservative speech nearly 70 percent of the time.
"More than any other modern Court, the Roberts Court has trained its sights on speech promoting conservative values," the authors found.
Polls show that both Democrats and Republicans believe that social media companies censor their users, however, the issue swings heavily conservative. Eighty-five percent of Republicans believe that social media companies censor speech the companies find objectionable, compared with 62 percent of Democrats, according to a June survey conducted by the Pew Research Center.
The survey also found that 4 in 10 Americans believe that the companies favor liberal speech, versus just 1 in 10 who believes the companies favor conservative speech.
In August, President Donald Trump blasted Google for allegedly suppressing conservative speech. In a post on Twitter, Trump wrote that "they are controlling what we can & cannot see. This is a very serious situation-will be addressed!"
Rep. Devin Nunes, R-Calif., the conservative chairman of the House Intelligence Committee, in July accused Twitter of censorship and threatened legal action against the company.
Perhaps most dramatically, Facebook, YouTube, Apple and the music platform Spotify removed content from right-wing conspiracy theorist and provocateur Alex Jones in August, accusing the talk show host of violating their terms of service. Indeed, MNN cited Jones's removal in a legal brief, saying it was an example of the heightened attention to the issue of First Amendment rights online.
The major social media companies, which either did not respond or declined to comment to CNBC, have said they do not censor speech based on political ideology.
In August, as the uproar from conservatives reached a fever pitch, Twitter CEO Jack Dorsey called into the radio show hosted by conservative commentator Sean Hannity.
"We do not shadow ban according to political ideology or viewpoint or content. Period," Dorsey said at the time.
For its part, Google released a statement saying that its search feature "is not used to set a political agenda and we don't bias our results toward any political ideology."
During an April hearing before the Senate's Commerce and Judiciary Committees, Facebook CEO Mark Zuckerberg was grilled by Sen. Ted Cruz, R-Texas, about whether Facebook considered itself a "neutral public forum."
"There are a great many Americans who I think are deeply concerned that that Facebook and other tech companies are engaged in a pervasive pattern of bias and political censorship," Cruz said.
In response, Zuckerberg said that Facebook is a "platform for all ideas."
contributed to this report.