I’ve always figured that witches and wizards have a variety of views on religion, just like in the real world. There are obviously Christian themes in the books; at the same time, Rowling has said that Hogwarts is a multifaith school. (Source: http://www.mtv.com/news/articles/1572107/jk-rowling-talks-about-christian-imagery.jhtml)
Since James and Lily were buried in the cemetery near a church, I figured that maybe they were members of that church. However, we can’t be sure how regularly they attended, as some people are members of a church but sometimes attend only on holidays while others attend more often. In addition to all of that, a person might have personal faith or other beliefs even if they don’t attend a church or other institution.
So, there are lots of possibilities.