FWIW, gag orders are closely scrutinized under the First Amendment. The big issue is that it is a prior restraint on speech:
>>>A "gag order" is the term for when a judge prohibits the attorneys, parties, or witnesses in a pending lawsuit or
criminal prosecution from talking about the case to the public. However, a court will scrutinize any gag order under the right of free expression, protected by the
First Amendment,
and applies a heavy presumption against its constitutional validity, as with any prior restraint. See Carroll v. Princess Anne. In
Nebraska Press Ass’n v. Stuart, the U.S. Supreme Court considered the following factors in analyzing the constitutionality of a gag order: “(a) the nature and extent of pretrial news coverage; (b) whether other measures would be likely to mitigate the effects of unrestrained pretrial publicity; and (c) how effectively a restraining order would operate to prevent the threatened danger [of an unfair trial for defendant].” In
that case, however, the Court found that a lower court’s gag order was justified because publicity of alleged shocking crimes would be widespread and would likely reach a jury,
impairing the defendant’s right to a fair trial.<<<(emphasis added)
www.law.cornell.edu
It appears to me that most of the gag order cases involve constraints on press reporting of crimes allegedly committed by a defendant in a case, and the effects the reporting might have on the defendant's right to a trail by an impartial jury.
The issue concerning a gag order on a
defendant is not as trivial as it might appear at first glance.
>>>Doing so would
raise tricky First Amendment issues as Mr. Trump makes another bid for the White House in a campaign that is partly defined by the criminal cases against him — and in which one of his rivals for the Republican nomination, former Vice President Mike Pence, is also a potential witness.
There is not a lot of precedent to guide Judge Chutkan’s decision. Gag orders are more typically imposed on defense lawyers instead of defendants, who under normal circumstances tend not to talk publicly about their cases out of self-interest.
And gag orders are more typically about preventing the jury from being tainted by hearing about the case outside the courtroom, while Mr. Smith has focused on the risk that Mr. Trump’s attacks may inspire threats or violence against participants in the process.<<<
Gag orders can forbid people to publicly discuss a case or aspects of it.
www.nytimes.com
Having said that, I expect Trump to file an appeal and I expect Trump to lose. Why do I expect this? I doubt that you'd see this stated directly in a written opinion from an appeals court, but Trump's statements are an attempt to undermine the rule of law itself, which is one of the foundations of our democratic system of government. Despite the First Amendment issues, I doubt that an appeals court would be persuaded to allow this to continue.
But, I could be wrong. This is just a best guess on my part.
