I'd like to study this further but I don't know what subject it would be classified as?
It is a combination of theology, history, language, sociology and anthropology. Researching information on people's believes and tracing their origin (which is one of the most common approaches used to debunk a belief) requires understanding its history and the content in which it comes from, as well as understanding the meaning and the way people communicate in the original language in which things originated.
If you look at documentaries that try to establish the veracity of a given belief, they always have to consult professionals in those areas (as well as tracing its origin). Additionally, if there are some believes that involve geography, architecture or science, for example, you might need to consult with people who specialize in those areas.
I don't think that there's one field that is dedicated to just Christian believes (unless you go to a Christian school, and their purpose is not exactly to be unbiased).