The NYCCHR informs the people of the city that it is a violation of the city's Human Rights Law for a covered person or entity to engage in, among other things:

Intentional or repeated refusal to use an individual's preferred name, pronoun or title. For example, repeatedly calling a transgender woman "him" or "Mr." after she has made clear which pronouns and title she uses ...

On top of that, pronoun compulsion goes beyond "him" v. "her" into made-up "gender-neutral" pronouns "ze" and "hir."  (Never heard of those before.  English already has a neuter third-person singular pronoun -- "it.")

Prof. Volokh, who specializes in the First Amendment, explains:

So people can basically force us -- on pain of massive legal liability -- to say what they want us to say, whether or not we want to endorse the political message associated with that term, and whether or not we think it's a lie.

We have to use "ze," a made-up word that carries an obvious political connotation (endorsement of the "non-binary" view of gender). We have to call people "him" and "her" even if we believe that people's genders are determined by their biological sex and not by their self-perceptions -- perceptions that, by the way, can rapidly change, for those who are "gender-fluid" -- and that using terms tied to self-perception is basically a lie. (I myself am not sure whether people who are anatomically male, for example, but perceive themselves as female should be viewed as men or women; perhaps one day I'll be persuaded that they should be viewed as women; my objection is to being forced to express that view.) We can't be required to even display a license plate that says "Live Free or Die" on our car, if we object to the message; that's what the court held in Wooley v. Maynard (1978). But New York is requiring people to actually say words that convey a message of approval of the view that gender is a matter of self-perception rather than anatomy, and that, as to "ze," were deliberately created to convey that a message.

Note in the middle of this paragraph that the free speech issue here is independent of where one stands on the underlying controversies.  CJLF has no position on those issues.

I do not have a shadow of a doubt that this policy is illegal.  But is it a crime?

The first three sections of the civil rights chapter of the federal criminal code are surviving remnants of the legislation of Reconstruction.  The first of them, 18 U.S.C. §241, punishes conspiracies "to injure, oppress, threaten, or intimidate any person ... in the free exercise or enjoyment of any right or privilege secured to him by the Constitution ...."  The second, §242, provides for punishment of anyone who "under color of any law, statute, ordinance, regulation, or custom, willfully subjects any person ... to the deprivation of any rights, privileges, or immunities secured by the Constitution ...."

Freedom of speech is, of course, a right secured by the Constitution against state action.  Although originally guaranteed by the First Amendment only against federal action, it has long been understood to be incorporated in the Fourteenth Amendment and protected there against abridgement by the states and their subdivisions.

In United States v. Lanier (1997), the Supreme Court addressed the problem of criminal liability for violating rights when those rights are not always crisply defined.  The person accused of the rights violation has rights too, one of which is "fair warning" of what the law prohibits.  The Court has grappled with this problem for a long time, at least as far back as the police brutality case of the infamous Sheriff Screws.  See Screws v. United States (1945).  (Yes, that was really his name.)

Lanier held that the "fair warning" standard is essentially the same as the "clearly established" standard for qualified immunity in civil cases.  (See pp. 270-271.)  The court reversed the holding of the Sixth Circuit that a precedent with "fundamentally similar" facts is required.  It quoted approvingly a statement from an earlier Seventh Circuit civil case.  "The easiest cases don't even arise.  There has never been ... a section 1983 case accusing welfare officials of selling foster children into slavery; it does not follow that if such a case arose, the officials would be immune from damages [or criminal] liability."  (p. 271)

Telling people what pronouns they must use is straight out of George Orwell's 1984.  This directive is to the First Amendment what the child sale hypothetical is to the Thirteenth.  Content-based restrictions on speech are generally prohibited by the First Amendment, and the exceptions are few and limited.  By no stretch of the imagination does this come within any of them.  Prof. Volokh notes the license plate compelled speech case, and this is far more of an intrusion than that one was.

In my opinion, this case is such a clear and egregious violation of civil rights as to be criminally prosecutable.  I don't expect the current Administration to actually do that, of course.  But there will be new sheriff in town come January.  The federal statute of limitations is five years.