It would be nearly impossible to find, let alone cite, a meaningful precedent to sanction a similar law in the United States. That's not to say there must be a precedent to make law, of course, but that if the U.S. Supreme Court were to vote in favor of something similar to this NZ law, they would be ignoring and superseding the countless arguments featured in landmark Constitutional law that, with great fervor, argue otherwise.

Freedom of speech includes expressions that will disagree, criticize, or offend; this applies to all citizens given that the very reason for its creation was precisely for the purpose of criticism towards the government.

"The sort of robust political debate encouraged by the First Amendment is bound to produce speech that is critical of those who hold public office." - Hustler v. Falwell

"It is a central tenet of the First Amendment that the government must remain neutral in the marketplace of ideas." - F.C.C. v. Pacifica

"The First Amendment does not guarantee that other concepts virtually sacred to our Nation as a whole, such as the principle that discrimination based on the basis of race is odious and destructive, will go unquestioned in the marketplace of ideas." - Texas v. Johnson

"When a man hath been laboring the hardest labor in the deep mines of knowledge, hath furnished out his findings in all their equipage, drawn forth his reasons as if it were a battle ranged, scattered and defeated all objections in his way, calls out his adversary into the plain, offers him the advantage of the wind and sun, if he please, only that he may try the matter by dint of argument; for his opponents then to skulk, to lay ambushments, to keep a narrow bridge of licensing where the challenger should pass, though it be valor enough in soldiership, is but weakness and cowardice in the wars of Truth." - John Milton

Most notably, look at the decision made in Hustler v. Falwell; as a result of being 'outrageously' parodied within the November issue of Hustler Magazine in 1983, respondent, and nationally known religious leader, political activist, and television evangelist Jerry Falwell filed to recover charges for invasion of privacy, libel, and unintentional infliction of emotional distress. The mock interview featuring Falwell's admittedly fictitious interview displayed his 'first time' as a "drunken, incestuous, rendezvous with his mother in an outhouse." Hustler included this parody due to having previously featured other Campari liqueur ads that would notoriously capitalize upon the "sexual double entendre of the general subject of first times." The District Courts dismissed claims of libel and invasion of privacy, but did uphold that Falwell would receive 100K in compensatory damages and 50K more in punitive.

Later, the Court of Appeals dismissed the First Amendment importance of the case by arguing it was irrelevant to the case which they saw as concerned not with protection of speech, but whether or not the defendants had acted intentionally or recklessly. This was met with resistance and granted certiorari by the Supreme Court because of its transparent involvement with First Amendment (free speech) issues.

It was decided 8-0 (justice Kennedy was not involved) that the intentional infliction of emotional distress as the basis or reason for which awards of damages are given is not consistent with the First Amendment of the U.S. Constitution.

This decision was important because it highlighted a few things. (1) the benefits of the free-flowing exchange of ideas are not limited to being positively affected by speech (2) inherent subjectiveness of being offended (i.e., not legally enforceable).

The Court has historically emphasized the fundamental importance and richness that freedom of speech and its inevitable consequences, both positive and negative, contribute to the "quest for truth and vitality as a whole," and that the State cannot restrict content based on what is desirable or not.

"There is no such thing as a false idea." - Gertz v. Robert Welch

TL;DR: it is both consistent and has been upheld that being offended is not a justified reason for receiving damage rewards. In other words, to be offended by an idea/symbol/group is not sufficient reasoning for speech to be suppressed in the United States. There are only a few caveats (e.g., speech meant to incite or imply imminent violence or danger) all of which demand strict scrutiny and a clear and compelling reason. None of which sophomorically indignant mahfeelz-laden feminist/new age rage-posts would pass.