Your religious background, or lack thereof, has no direct effect on your application. Some candidates have leadership positions in church-based organizations. That type of leadership counts much as other types of leadership. However, you can be an atheist and it won't matter in terms of your getting an appointment.
At USNA, there are numerous opportunities to practice your religion. There are 6 chaplains, including Catholic, various Protestant denominations, and occasionally Jewish rabbis or Muslim Imans. After plebe summer, you can go out in town to the church of your choice. Chapel hasn't been mandatory for about 45 years and not going to church is fine.