Your religious beliefs do not protect you from refusing to participate in employment screening.
A polygraph is going to be required in any line of law enforcement. I have taken one when I was in the application process. The purpose of it is to establish a pattern of behavior. Most of the time they are not interested in finding out about every little thing you have done (unless it is a felony) but to see if you show a pattern of disturbing behavior (frequent drug abuse, theft, etc). If you honestly have nothing to hide and you tell the truth, you will be fine. If you refuse to take one, then you might want to reconsider if you really want this line of work. This job might require you to do things you otherwise might not believe in either.
The purpose of the polygraph is also to weed out any individual who is a criminal, and who has gotten away with committing crimes. These people do slip through the cracks and a polygraph can generally tell if a person is lying. They are surprisingly accurate. I am usre you would not want a person who has killed, stole, assaulted, dealt drugs, being a police officer would you?