The order certifying the class action and the ruling provide circumstantial details that would bear on the applicability of that reasoning. The opinion frames the question as:
Does the United States Constitution permit the New York City Police
Department (the "NYPD") to require an observant Muslim woman to remove
her hijab when sitting for an arrest photo? The Court holds that it
does not.
The agreed-to settlement includes instructions to police that are broader:
A religious head covering worn pursuant to a sincerely held religious
belief can be retained by the prisoner while in the custody of the
Department. However, the religious head covering must be temporarily
removed when conducting the mandatory Department search for weapons
and/or contraband, but will be returned to the prisoner after that
search unless the head covering presents a risk to the safety of the
prisoner or others.
The First-Amendment part of the ruling is that
Clark and Aziz have no alternative means of exercising their right to
wear a hijab in public, at all times. The Policy, although sometimes
inconsistently applied, still requires that Clark and Aziz remove
their hijabs and makes their photographs available to men. The Court
agrees with Plaintiffs that permitting observant Muslim women to wear
a hijab while being photographed as part of booking procedure would
have reasonably accommodated their beliefs and also would be less
burdensome on the NYPD. Indeed, snapping a Booking Photograph of an
arrestee with her religiously compelled covering would expend fewer
resources than “requir[ing] dialogue with arrestees and additional
time spent negotiating removal.”
The First Amendment is equally available to males and females, and to Muslims and non-Muslims. This ruling cannot be interpreted to mean that only women or only Muslims have this right to religious expression.
The courts have also declined to engage in religion-evaluation whereby some beliefs are certified as "true religion" and others are "false religion". See Schwarzentruber v. Gunite, where an employee was required to cover up his racist tattoos on the job, and sued on First Amendment accommodation grounds. The court states the relevant legal principle regarding such a suit:t
To establish a prima facie case of religious discrimination, a
plaintiff must show that (1) he has a sincere religious belief,
observance or practice that conflicts with an employment requirement;
(2) he informed his employer of the conflict; and (3) the religious
practice was the basis for the adverse employment decision.
Plaintiff lost the case because he
cannot show that he holds a sincere religious belief that conflicts
with an employment requirement.
even though he alleges that
the "Firey Cross" tattooed on his arm is one of that church's seven
sacred symbols
The crux of the defendant's failure is that he
does not present admissible evidence, or even contend without
evidence, that being required to cover up his tattoo at work conflicts
with his religious beliefs, or that he told Gunite about any conflict
with his beliefs and Gunite's demand that he cover his tattoo. Mr.
Swartzentruber doesn't satisfy the first and second elements of a
prima facie case.
The atheist male hat-wearer would at a minimum have to contend that he has a deep-seated belief about the nature of the universe that he must (whatever the claim is). It is settled First Amendment law that a "religious belief" does not have to be theistic. This page sets forth the case law and reasoning leading to the conclusion that atheism must be treated as a religion. See Kaufman v. McCaughtry and citations therein. That court observes that
a religion, for purposes of the First Amendment, is distinct from a
“way of life,” even if that way of life is inspired by philosophical
beliefs or other secular concerns. A religion need not be based on a
belief in the existence of a supreme being (or beings, for
polytheistic faiths) nor must it be a mainstream faith
Without venturing too far into the realm of the philosophical, we have
suggested in the past that when a person sincerely holds beliefs
dealing with issues of “ultimate concern” that for her occupy a “place
parallel to that filled by ․ God in traditionally religious persons,”
those beliefs represent her religion. We have already indicated that
atheism may be considered, in this specialized sense, a religion.
See Reed v. Great Lakes Cos. (“If we think of religion as taking a
position on divinity, then atheism is indeed a form of religion.”).
Kaufman claims that his atheist beliefs play a central role in his
life, and the defendants do not dispute that his beliefs are deeply
and sincerely held.
This sketches the claims that a person would have to make in order to rely on a Free Exercise exception to a general rule.