The Equal Employment Opportunity Commission (EEOC), which enforces Title VII of the Civil Rights Act of 1964, recently issued explicit guidance on "Religious Garb and Grooming in the Workplace: Rights and Responsibilities."
The bottom line is that employers must respect and accommodate religious garb and grooming in their places of business unless they can prove that doing so would pose "an undue hardship." And religion is defined very broadly as encompassing not only recognized, formalized faiths but also "religious beliefs that are new, uncommon, not part of a formal church or sect, only subscribed to by a small number of people, or may seem illogical or unreasonable to others."
Fortunately, the guidance — which you can read by clicking here — gives various examples of how religious accommodations should be handled and also lists instances in which an "undue hardship" exception might apply.