But a NY judge has ruled that the president's account, and those of other government officials, are public forums and that blocking Twitter users for their views violated their right to free speech under the First Amendment of Constitution.
"In so holding, we reject the defendants' contentions that the First Amendment does not apply in this case and that the President's personal First Amendment interests supersede those of plaintiffs".
The plaintiffs, working with the Knight First Amendment Institute at Columbia University, sued Trump and White House director of social media Daniel Scavino in July.
The ruling reaffirmed the conception most American citizens had over what constitutes a public forum in an age of interconnectedness, despite Twitter being a private company-elected officials' social media handles are maintained by government officials on the government's payroll.
Serving senators across the major political parties have also been accused of frequently using the block button against critics.
Under the ruling, Buchwald did not order Trump to unblock his followers, saying a finding that clarifies the law is sufficient to resolve the dispute.
The Justice Department defended Trump's Twitter activity, contending that muting is within the president's "associational freedoms".
"Given that no government office is above the law, we assume that the president and [Daniel] Scavino will remedy the blockade that we have considered unconstitutional", which the plaintiffs have to request to Trump, says Buchwald.
Turkish currency drops to record low against dollar
A photo illustration shows a $100 banknote against Turkish lira banknotes of various denominations, January 7, 2014. No announcement, however, has come from the Central Bank or others.
The Department of Justice said in a statement that it "respectfully" disagrees with the ruling and is considering how to proceed.
"This case requires us to consider whether a public official may, consistent with the First Amendment, "block" a person from his Twitter account in response to the political views that person has expressed and whether the analysis differs because that public official is the president of the United States", she wrote.
Even if it's argued that the ruling is narrow and only meant to apply to public figures (maybe even arguing that it applies only to the US president), that still has implications for Twitter's enforcement policy.
But to block someone both prevents that person from seeing tweets and from responding to them, preventing them from even accessing a public forum.
Genevieve Lakier, a professor at the University of Chicago Law School who helped write a friend-of-the-court brief filed by First Amendment scholars, welcomed Wednesday's decision.
However, the Federal District Court for the Southern District of NY found that this was not the case.
The key question facing the judge was whether Mr. Trump's account amounted to a forum like a public park or a town square - places the Supreme Court has held to be First Amendment spheres of interaction.
In what seems to us like the weakest part of the decision, Buchwald concludes that the "interactive space" around Trump's tweets qualifies under this standard. Her idea for a settlement: perhaps Trump could mute, rather than block, his critics.