"Bona fide occupational requirement" is a specific legal term in this context. You can't discriminate based on something like age, sex, gender, religion or disability unless the position has a "bona fide occupational requirement" that can override that.

For example, poor eyesight is a disability, but good eyesight is a requirement for pilots. Therefore, it would not be discrimination to reject a person with poor eyesight.

In your case, unless they can make the argument that being a member of their specific religion is an occupational requirement (which they can't unless you're trying to become a priest or something), then it's illegal for them to do that.