Professor Turley (read Bio) presents his case on his popular legal blog as follows (emphases mine):

‘New York Supreme Court Justice Juan Merchan this week became the latest court to impose a gag order on former president Donald Trump with a stinging order that found a history of Trump attacks that threatened the administration of justice. The order will bar public criticism of figures who are at the center of the public debate over this trial and the allegation of the weaponization of the legal system for political purposes, including former Trump counsel Michael Cohen, former stripper Stormy Daniels, and lead prosecutor Matthew Colangelo. Trump is still able to criticize Manhattan District Attorney Alvin Bragg and Merchan himself.  What is most striking is the protection of Cohen who continues to goad Trump in public attacks..’.

Jonathan concludes,

 

There is a division on courts in dealing with such challenges involving politicians. For example, a court struggled with those issues in the corruption trial of Rep. Harold E. Ford Sr. (D–Tenn.). The district court barred Ford from making any “extrajudicial statement that a reasonable person would expect to be disseminated by means of public communication,” including criticism of the motives of the government or basis, merits, or evidence of the prosecution.

The United States Court of Appeals for the Sixth Circuit rejected the gag order as overbroad and stressed that any such limits on free speech should be treated as “presumptively void and may be upheld only on the basis of a clear showing that an exercise of First Amendment rights will interfere with the rights of the parties to a fair trial.”

This order allows for criticism of the case and both Merchan and Bragg. However, you have key figures like Cohen and Coangelo who are already central figures in this political campaign. In Cohen’s case, he has actively engaged in a campaign to block Trump politically and has done countless interviews on this case as part of the legal campaign.

While courts routinely rubber stamp such orders (and Trump’s history will reinforce the basis of the Merchan order), I would still try to appeal it.  The odds always run against challenging such orders and appellate courts are disinclined to even review such orders. However, there is a legitimate free speech concern raised by this order that should be reviewed by higher courts.’