the U.S. Court of Appeals for the Third Circuit just held in Webb v. City of Philadelphia (some paragraph breaks added):

[Kimberlie] Webb requested permission from her commanding officer to wear a headscarf while in uniform and on duty. The headscarf (a khimar or hijaab) is a traditional headcovering worn by Muslim women. Webb's headscarf would cover neither her face nor her ears, but would cover her head and the back of her neck. Her request was denied in view of Philadelphia Police Department Directive 78, the authoritative memorandum which prescribes the approved Philadelphia police uniforms and equipment. Nothing in Directive 78 authorizes the wearing of religious symbols or garb as part of the uniform....

Title VII of the 1964 Civil Rights Act prohibits employers from discharging or disciplining an employee based on his or her religion. "Religion" is defined as "all aspects of religious observance and practice, as well as belief, unless an employer demonstrates that he is unable to reasonably accommodate to an employee's ... religious observance or practice without undue hardship on the conduct of the employer's business." To establish a prima facie case of religious discrimination [on this "religious accommodation" theory -EV], the employee must show: (1) she holds a sincere religious belief that conflicts with a job requirement; (2) she informed her employer of the conflict; and (3) she was disciplined for failing to comply with the conflicting requirement.

Once all factors are established, the burden shifts to the employer to show either it made a good-faith effort to reasonably accommodate the religious belief, or such an accommodation would work an undue hardship upon the employer and its business.... An accommodation constitutes an "undue hardship" if it would impose more than a de minimis cost on the employer. Both economic and non-economic costs can pose an undue hardship upon employers; the latter category includes, for example, violations of the seniority provision of a collective bargaining agreement and the threat of possible criminal sanctions.

In the City's view, at stake is the police department's impartiality, or more precisely, the perception of its impartiality by citizens of all races and religions whom the police are charged to serve and protect. If not for the strict enforcement of Directive 78, the City contends, the essential values of impartiality, religious neutrality, uniformity, and the subordination of personal preference would be severely damaged to the detriment of the proper functioning of the police department. In the words of Police Commissioner Sylvester Johnson, uniformity "encourages the subordination of personal preferences in favor of the overall policing mission" and conveys "a sense of authority and competence to other officers inside the Department, as well as to the general public."

Commissioner Johnson identified and articulated the police department's religious neutrality (or the appearance of neutrality) as vital in both dealing with the public and working together cooperatively. "In sum, in my professional judgment and experience, it is critically important to promote the image of a disciplined, identifiable and impartial police force by maintaining the Philadelphia Police Department uniform as a symbol of neutral government authority, free from expressions of personal religion, bent or bias." Commissioner Johnson's testimony was not contradicted or challenged by Webb at any stage in the proceedings....

As a para-military entity, the Philadelphia Police Department requires "a disciplined rank and file for efficient conduct of its affairs." Commissioner Johnson's thorough and uncontradicted reasons for refusing accommodations are sufficient to meet the more than de minimis cost of an undue burden.

For more details, including how the court dealt with various relevant precedents, both from the Supreme Court and from other circuits that had confronted similar problems, have a look at the opinion, which is pretty readable and not too long.

Thanks to Joel Sogol for the pointer.