Xjyuk

I read today about the Anti-Censorship Activists in New York (Warning! NSFW pictures inside link) who protested against Facebook while being totally nude out in the street.

I'm also pretty sure public nudity is not allowed in the USA.

How come they were not arrested or at least warned by police? Is there some exception to the law?

Public nudity is illegal in New York as it is in almost every U.S. jurisdiction. And, if the police had arrested the nude protesters, the arrests probably would have been upheld in court, because a ban on nudity in public would probably be viewed as a time, place and manner restriction on the freedom of speech which is constitutionally valid.

For example, the Ninth U.S. Circuit Court of Appeals recently upheld San Francisco’s public nudity ordinance in Taub v. City and County of San Francisco (2017). As the court in that case explains in a factually very similar case:

Public nudity is not inherently expressive, but it may in some
circumstances constitute expressive conduct protected under the First
Amendment. City of Erie v. Pap’s A.M., 529 U.S. 277, 289 (2000)
(O’Connor, J.) (plurality opinion). Even if Plaintiffs’ public nudity
at political rallies was entitled to First Amendment protection,
however, we hold that the challenged ordinance is a valid, content
neutral regulation as applied to Plaintiffs’ expressive conduct under
United States v. O’Brien, 391 U.S. 367 (1968). O’Brien is the applicable test here because the ordinance is aimed at “the conduct
itself, rather than at the message conveyed by that conduct.” United
States v. Swisher, 811 F.3d 299, 312 (9th Cir. 2016) (en banc).

But, while a court would have made that distinction, the public, which is used to the idea that protesters shouldn't be arrested for protesting, might not.

However, under U.S. law, the police are never required to enforce any law. See Castle Rock v. Gonzales.

In this case, the NYPD probably just decided that the benefit that the city could have secured by enforcing this law wasn't worth it, in terms of costs
to the city, making the city safer, and the public image of the NYPD.

For example, the city would have had to pay to book and incarcerate the protestors in crowded and expensive jails, and then fight expensive legal battles in petty misdemeanor court prosecutions to defend the anti-nudity law, an issue that isn't a priority for the city's scarce resources at the moment. There is always a risk that any mass arrest could turn a peaceful gathering into a dangerous riot. And, those anti-nudity laws are on the books primarily do deal with drunks and flashers, not anti-censorship protestors. A loss in court in one of these cases (as unlikely as it might be) would undermine the ability of the NYPD to enforce the anti-nudity law in the kind of cases it was actually intended to address, in which a first amendment challenge would almost surely not succeed.

Arresting a bunch of naked people wouldn't be fun and would look bad in on the nightly news, and getting naked protestors off the street wouldn't make NYC a safer place. So, they chose not to enforce a law that they could have enforced if they had decided to do so.

Not warning the protestors that they were violating the law would also not have served the NYPD's purpose. If they gave a warning and then didn't follow up when the warning was ignored, that would undermine the NYPD's credibility in future protests. And, even a warning could cause fear to spread throughout the crowd increasing the risk of a peaceful protest turning into a dangerous riot.

Training materials for law enforcement officers reflect these concerns (see internal pages 55-56 in the linked materials):

Mass arrests during demonstrations in Washington, D.C., New York City
and other major locales have been criticized. In some cases, the
protest activity, while unlawful, was not necessarily violent.
Complaints included that law-abiding protestors and passersby were
rounded up and detained along with violators in overly broad sweeps.
The negative impact of these media images damages the public
perception of the police operation, as it draws into question the
reasonableness and proportionality of the police response. Subsequent
litigation has proven to be particularly costly. In most instances
only a tiny number of those arrested actually appear in court and most
of those are charged with offenses that would not normally attract an
arrest or detention (Temple 2003). Law enforcement agencies need to
ensure that operational commanders have a clear and uniform
understanding of the mass-arrest policy to be followed.

Litigation has included criticism of understaffed prisoner processing
operations that, when overwhelmed, led to inordinate detention without
charge. This occurred at the Republican National Convention in 2004
and led to court instructions and fines for inordinate delay in
processing detained persons (New York Times 2004).

Research into recent mass-arrest operations shows that arrests are
easily accomplished. The areas where problems arise with sudden, but
now predictable, regularity are

• The quality of evidence available to pursue prosecution against each individual;




• The logistics of transporting and handling large numbers of prisoners;




• Allowing legal and medical access;




• An inordinate delay in arranging for release or bringing persons to court;




• Not enough police on duty to cope with the above—process centers are frequently overwhelmed at an early stage due to lack of resources; and




• In some cases, the courts have ruled that top police officials can be held personally liable for damages or actions.

Mass arrests are generally advisable only when all alternative tactics
have either been tried unsuccessfully or are unlikely to be effective
under specific circumstances. When mass-arrest tactics are used,
evidence against each individual prisoner must be available to support
the charges.

Arrest tactics training is a critical component of mission success.
The training must address the spectrum of event types: non-violent
protest, non-violent civil disobedience, passive resistance (including
the use of chains, sleeves and other devices to impede arrest) and
violent confrontation. Training must recognize the difference between
two arrest scenarios:

• Arrest tactics where police are in control of the environment and have time to plan and implement the arrests or dispersal in a
  controlled manner, (e.g., at a sit-down protest); and




• Arrest tactics where police do not control the environment (e.g., when police are trying to re-establish control of the environment by
  arresting violent demonstrators).

Pressure point techniques, in conjunction with empty hand control,
efficient handcuffing, and arrestee escort methods should be included
to remove protesters humanely while minimizing risk of injury to
protestors and police. Such tactics should be part of ongoing and
regular refresher training to ensure officers maintain efficiency.

Tactical commanders present at many of the demonstration events
reviewed by PERF agreed that unless the actions of certain protestors
necessitate their removal, the better course of action is not to
expend resources on arrests. For example, in instances where sleeping
dragons are situated so as to disrupt traffic, it may be less of a
drain on already-thin operational resources to simply monitor them and
reroute traffic. Moreover, protest organizers have on occasion
scheduled “officer intensive” diversions just before they undertake
more violent or destructive actions elsewhere, calculating that the
police would be too busy handling the mass arrest to respond to
further actions.

Pretty much anyone with common sense knows that it isn't smart to disturb a sleeping dragon in the middle of an intersection in New York City. Trying to try to arrest a dragon is very hard and dragons can afford to pay good lawyers with their treasure hordes. But, police also have to consider more difficult choices like the choices presented by this nude protest.

Any anti-nudity law is subordinate to the First Amendment to the US Constitution. The action clearly constitutes political expression, which is protected. Not every imaginable action can be excused if done in the name of political expression, so enforcement would involve a "strict scrutiny" analysis. That is, when a fundamental right is involved, a law has to further a "compelling governmental interest," it must be "narrowly tailored" to achieve that interest, and it must be the "least restrictive means" of achieving the purpose. The law says

A person is guilty of exposure if he appears in a public place in such
a manner that the private or intimate parts of his body are unclothed
or exposed.  For purposes of this section, the private or intimate
parts of a female person shall include that portion of the breast
which is below the top of the areola.  This section shall not apply to
the breastfeeding of infants or to any person entertaining or
performing in a play, exhibition, show or entertainment.

A political demonstration can be considered a kind of exhibition, and should be so construed when strictly scrutinized.

Laws against public nudity, usually termed "indecent exposure", are not federal laws in the US. They are either sate laws, or in many cases, local laws (city, county, or other local jurisdiction). Therefore what is prohibited under such laws, and where they apply, vary significantly.

Also, in a number of jurisdictions, courts have ruled that arrests for exposure of the female breast are not constitutional when males may go shirtless on Equal Protection grounds, or on the grounds that the particular instance was expressive conduct, and was protected by the First Amendment. I believe that the law linked in the answer by user6726 is one that has been modified by a court ruling.Thhis law.se question discussed that issue in some detail.

Note that even protected speech (and expressive conduct) is subject to regulation of "time, place, and manner", provided that such regulations do not unduly burden expression, and are content-neutral. There is a lot of case law on what regulations are and are not constitutional, far more than can be summarized in a single answer here. If police had arrested the nude protesters described in the question, the state might have defended the arrest as a regulation of the "manner" of expression.

Note also that what actions are, and what are not "expressive conduct" is subject to review in such cases. US Courts often ask what is the "particularized message" conveyed by specific conduct, and how does that conduct convey that message. In some cases courts have ruled that conduct which is asserted to be "expressive" is not so. (For example, wearing a hood as part of a Klu Klux Klan uniform has been held not to be expressive conduct.)

Thus, if the protesters had been prosecuted, it is not clear how the courts would have treated a claim that their conduct was protected expression. The NY authorities choose not to enforce the law on the books in this case, no doubt knowing that a potentially complex case would result. They have wide discretion on when to enforce the law, and when not to.