Title VII of the Civil Rights Act of l964 prohibits employers from discriminating against individuals because of their religion in hiring, firing, and other terms and conditions of employment. The Act also requires employers to reasonably accommodate the religious practices of an employee or prospective employee, unless to do so would create an undue hardship upon the employer (see also 29 CFR l605). Flexible scheduling, voluntary substitutions or swaps, job reassignments and lateral transfers are examples of accommodating an employee's religious beliefs.  Section 703(a)(1) of the Civil Rights Act of 1964, Title VII, 78 Stat. 255, 42 U.S.C. s 2000e-2(a)(1), makes it an unlawful employment practice for an employer to discriminate against an employee or a prospective employee on the basis of his or her religion. A guideline of the Equal Employment Opportunity Commission (EEOC), 29 CFR s 1605.1(b) (1968), required, as the Act itself now does, 42 U.S.C. s 2000e(j) (1970 ed., Supp. V), that an employer, short of "undue hardship," make "reasonable accommodations" to the religious needs of its employees.
Trans World Airlines, Inc. v. Hardison  432 U.S. 63, *66, 97 S.Ct. 2264, **2268 (U.S., 1977)

Employers cannot schedule examinations or other selection activities in conflict with a current or prospective employee's religious needs, inquire about an applicant's future availability at certain times, maintain a restrictive dress code, or refuse to allow observance of a Sabbath or religious holiday, unless the employer can prove that not doing so would cause an undue hardship.

An employer can claim undue hardship when accommodating an employee's religious practices if allowing such practices requires more than ordinary administrative costs. Undue hardship also may be shown if changing a bona fide seniority system to accommodate one employee's religious practices denies another employee the job or shift preference guaranteed by the seniority system.

An employee whose religious practices prohibit payment of union dues to a labor organization cannot be required to pay the dues, but may pay an equal sum to a charitable organization.

Mandatory "new age" training programs, designed to improve employee motivation, cooperation or productivity through meditation, yoga, biofeedback or other practices, may conflict with the non-discriminatory provisions of Title VII. Employers must accommodate any employee who gives notice that these programs are inconsistent with the employee's religious beliefs, whether or not the employer believes there is a religious basis for the employee's objection.

See also: How To File A Charge of Employment Discrimination