That's the question in Webb v. City of Philadelphia; this decision provides some background, and dismisses some collateral claims on procedural grounds, but does not dispose of the substantive question.
Title VII generally obligates employers to reasonably accommodate employees' religious practices, so long as doing so doesn't cause an undue hardship to the employer (something caselaw has defined as anything more than a minimal hardship). Webb's claim is chiefly that her religious practice of wearing the khimar (which, I'm told, is "a headscarf worn by observant Muslim women that hangs down to just above the waist") must therefore be accommodated.
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- Muslim Policewoman Has No Right To Wear a Religious Headscarf on the Job,
- Ban on Headgear, Including Religious Headgear, in Court:
- Religious Accommodations:...
- The Odd Assumption of Islam as Monolith:
- Muslim Policewoman Barred from Wearing Khimar on the Job:
- Does a Female Muslim Police Officer Have a Right To Wear a Khimar?