Yes, according to an EEOC informal discussion letter, an employee may be entitled to an exemption from a mandatory vaccination policy as a religious accommodation unless, under the circumstances, it would result in an undue hardship to the employer. However, the employer may require that the employee provide third-party verification of her sincerely held religious belief or practice from a church official, church member, or other person aware of her religious belief or practice. When an employer makes a reasonable inquiry for such information, the employee must cooperate, or she may not be entitled to an accommodation.
When employees are exempted from the mandatory flu shot, employers may impose other infection control measures, such as a mask requirement, if not done for retaliatory or discriminatory reasons.
Source: EEOC Informal Discussion Letter, Title VII: Vaccination Policies and Reasonable Accommodation, reported in Employment Law Daily, January 21, 2013.