Does my coworker have a right to proselytize at work?

You should complain to your employer, explaining that your coworker's proselytizing is making you uncomfortable and that you have asked her to stop. Her comments might constitute illegal harassment, which gives your employer a duty to step in.

Religious discrimination is illegal under Title VII. At the most basic level, this means employers may not make decisions based on an employee's religious beliefs (or lack thereof). For example, an employer may not promote only Christians, refuse to hire Sikhs, or treat atheists more harshly than religious employees. Harassment on the basis of religion (or lack of religious belief) also violates Title VII. And, Title VII requires employers to accommodate their employees' sincerely held religious beliefs and religious practices.

The intersection of these last two requirements is where you and your employer find yourselves -- and at this intersection, it can be tough to figure out who has the right of way. On the one hand, your employer has a legal duty to accommodate your coworker's religious beliefs and practices. It seems clear that your coworker sincerely believes that her religion requires her to proselytize. On the other hand, your employer also has a legal duty to prevent and remedy harassment, including harassment based on religion.

Harassment is offensive, unwelcome conduct, based on a protected category (such as religion), which is severe or pervasive enough to alter the terms or conditions of employment. You've told your coworker that her comments are unwelcome, and it sounds like they have been persistent and frequent enough to change the conditions of your job. At this point, once you complain to your employer and make clear that you find your coworker's conduct offensive and disruptive, your right to work free of harassment most likely trumps your coworker's right to practice her religion at work. Your employer is not required to accommodate religious conduct that creates an undue hardship, and conduct that harasses other employees or customers imposes this kind of burden on the employer.

If no one found your coworker's comments offensive, or your coworker took a softer tack (such as putting up a poster or wearing a button proclaiming her faith), the outcome could well change. In this situation, your coworker's right to practice her religion might not create an undue burden. However, once an employee's religious practice crosses the line and becomes severe and pervasive, the employer has a duty to act.