Federal law (Title VII of the Civil Rights Act) and the laws of most states prohibit employers from engaging in religious discrimination -- that is, discriminating based on an applicant's or employee's religion. At the same time, however, these laws sometimes require employers to accommodate an employee's religious beliefs or practices -- in other words, to take the employee's religion into account when making decisions.
This apparent contradiction comes from the fact that religion is not a characteristic in the same way as race or age: Instead, it is a set of practices and beliefs. And, in some religions, believers want -- or believe their religion requires them -- to express their faith by, for example, not cutting their hair, wearing certain clothing or religious items, or telling others of their beliefs.
Discrimination Is Prohibited
The law protects employees from discrimination on the basis of their religion. For example, an employer may not refuse to hire Muslims, promote only Baptists, fire all Mormons, and so on. This protection doesn't only protect members of large, organized religions: It protects employees from discrimination based on their moral or ethical beliefs about right and wrong, as long as those beliefs are sincerely held with the strength of traditional religious views.
Employees who are not religious are also protected, if they are treated differently because of religion. For instance, an employer may not refuse to hire applicants who don't share the founder's religious faith or refuse to promote employees who are atheists.
Your Right to an Accommodation
If you have a sincere religious belief that conflicts with an employment rule or requirement, the law requires your employer to accommodate your beliefs, working with you to find a way around the conflict. This might mean, for example, agreeing not to schedule you to work on your Sabbath day or relaxing a company dress code so that you can wear religious garments.
The employer does not have to provide the accommodation you request, but must work with you to come up with a plan that will work. However, an employer need not provide an accommodation that will create an undue hardship for the company. For example, if an accommodation would impose more than minor costs, substantially harm the morale of other employees, or create a significant disruption in work routines, the employer need not provide it.
Workplace Expression of Religious Beliefs
Some employees want to express their religious beliefs in the workplace by, for example, using religious language (such as "God bless you" or "Praise the Lord") when communicating with others or attempting to proselytize coworkers. In these situations, it can be difficult to balance the rights of the religious employee with the rights of others who do not share those beliefs. An employee who isn't allowed to express sincere religious beliefs may feel discriminated against; at the same time, an employee who is unwillingly subjected to a coworker's religious statements may feel harassed.
According to the EEOC, employers must allow employees to engage in religious expression at work as long as it doesn't create an undue hardship. And employers may not restrict religious expression more heavily than other forms of expression that have a similar impact on workplace efficiency. (For example, if a company allowed employees to engage in pitched arguments over politics, it would be difficult for that company to justify a complete crackdown on discussions of religion.)
It's not entirely clear what these rules mean in practice. Courts have made diverse rulings when employees have sued because they weren't allowed to express their religious beliefs at work. Some courts have held that an employer doesn't have to accommodate an employee's religious expression when it could constitute harassment against other employees or it goes against the employer's diversity or nondiscrimination policies. On the other hand, some courts have found in the employee's favor if his or her behavior was merely "annoying" or created discomfort for others.