It's an ethical question but if the new nurse stated her request was for religious accommodation, regardless if it is not a typically affiliated recognized denomination, but the church leader states that 'it should not be a problem for the new church member'
then the employer/manager is not obligated to honor the request and perhaps may want to discuss her findings with the new employee.
Since healthcare is a 24/7/365 obligation and this is a new not-yet-out-of-probation employee, the manager may want to redirect this special request to human resources to ensure that any legal obligations for accommodations are met. (but include the information obtained from the church representative that is contrary to the new employee's statements). Did she offer an alternative such as working every Saturday or every statutory holiday in exchange for another employee to work her Sundays?
I know some nurses and healthcare workers who practice the Orthodox Jewish faith and observe the Sabbath from Friday sundown to Saturday sundown. In exchange for not working on Saturdays these employees will work Sundays and an employee who would prefer to work Saturday over Sunday works the Saturdays (they also exchange religious holidays as one is a practicing Christian) . It does not put a burden on the employer as the shifts are covered by equivalent employees. (This was in a position that requires 2 weekends worked a month, the employer reworded the policy to "four weekend days" a month instead of two full weekends...everyone was happy)
From the EEOC "Religious discrimination involves treating a person (an applicant or employee) unfavorably because of his or her religious beliefs. The law protects not only people who belong to traditional, organized religions, such as Buddhism, Christianity, Hinduism, Islam, and Judaism, but also others who have sincerely held religious, ethical or moral beliefs. Religious Discrimination & Reasonable Accommodation
The law requires an employer or other covered entity
to reasonably accommodate an employee’s religious beliefs or practices, unless doing so would cause more than a minimal burden on the operations of the employer's business. This means an employer may be required to make reasonable adjustments to the work environment that will allow an employee to practice his or her religion.
Examples of some common religious accommodations include flexible scheduling, voluntary shift substitutions or swaps, job reassignments, and modifications to workplace policies or practices... Religious Discrimination & Reasonable Accommodation & Undue Hardship
An employer does not have to accommodate an employee’s religious beliefs or practices if doing so would cause undue hardship to the employer. An accommodation may cause undue hardship if it is costly, compromises workplace safety, decreases workplace efficiency, infringes on the rights of other employees, or requires other employees to do more than their share of potentially hazardous or burdensome work." (source: Religious Discrimination