My supervisor often holds religious events like prayer meetings and Bible study groups.
Because religion is such an important part of many people's lives, it is not surprising that it will end up playing a role for them where they work. They cannot be expected to "turn off" their religion when they punch a time clock at the start of the day, so the sight of people praying, of people's religious symbols, and of people reading from religious scriptures should be neither surprising nor troubling.
People's involvement in religion can also lead them to organize religiously-oriented groups at work, for example Bible study groups or prayer groups. Such social and religious organizations are not very different in nature from a company softball team or similar religious clubs organized by students all across the country. Their mere existence is not only not a problem, but is protected as the free exercise of people's religions.
When a company is private, the owners of that company are allowed to permit such groups to use company facilities for meetings, for copying documents, etc. If the office is part of the government, similar arrangements must be made for religious groups if they are also made for secular groups (again, like a softball team). If no accommodations are made with secular groups, then none are required for religious groups either.
Circumstances change, however, when your supervisor or manager is heavily involved but you are not; or, even worse, if you have expressed an opposition to or even disdain for such religious groups. If a manager or owner suggests by deed or word that some particular faith is favored, that sends the wrong signals to those employees who do not share that faith. In such a situation, you might be afraid that you will be treated differently because of your failure to participate in the same religious events as everyone else. You may be concerned that your evaluations will be based in part on your lack of participation in religion.
This is not an entirely idle fear. People treat religion much more seriously than they do other activities, viewing non-participants with more suspicion and negativity than they do non-participants in things like sports (though football in Texas is a notable exception). Thus, a person who isn't interested in joining the company softball team isn't likely to be ostracized and receive poor performance reviews, but a person who rejects participation in Bible study or prayer might.
Such discrimination can be deliberate, but it certainly doesn't need to be. Because people view religion as an important, if not the only, source of things like morals, values, and purpose in life, they can quickly assume (erroneously) that people who have no religion (or even just don't have their religion) must somehow lack the proper morals and values. This can influence them to judge that person in a more negative manner, no matter what the evidence before their eyes may be. All of our interpretations of the evidence before us are influenced to one degree or another by our prejudices; this is no different, although religious prejudices can have a perniciously strong hold.
How you handle yourself when faced with popular Bible study or prayer groups where you work will depend a lot upon your specific circumstances. If you have a good relationship with your supervisor and feel comfortable with it, you should approach her privately, explain that you don't wish to participate, and indicate that you hope it won't affect how your are evaluated as an employee. That will, hopefully, be the end of that although you may have to deal with hard feelings on the part of other participants and, perhaps, overzealous attempts to get you to change your mind.
If, however, your supervisor is not sympathetic and you feel like you are getting signals that your failure to participate in religious activities at your job is affecting how you are being treated professionally, then you are in a more difficult situation. One of the most important things you must do is keep a record of everything that happens jot down the date, time, and content of whatever hints, comments, or other signals you see. Some may be nothing, but having evidence of a persistent pattern over an extended period of time may prove useful.
As much as possible, try to handle the situation within the company and with as much politeness as possible. Speak to supervisors, managers, and whomever else you can about your concerns until you find someone who will take you seriously. Here, too, you should keep a record of the meetings and what was said. If at some point you feel that you are being evaluated worse that you deserve and think it is because of religion, you may want to talk to a lawyer. At this point, your diligence at keeping records should prove invaluable because they will help a lawyer decide if you have a case and if you do go to court, they will serve as important evidence.