I am applying to a Christian University, and they have requested that in my CV I include my religious background. I have no issue with doing this, so I plan to simply make the appropriate additions to my existing CV. However, I'm not really sure what I should include. Obviously, only I know my religious beliefs and background, but I'm not sure if they are asking for things like church attendance, or a very brief statement of faith so any suggestions would be appreciated.
In addition to the answers given by others, let me suggest one additional tactic: read some CVs of current faculty.
People who have already been at the university for a while have clearly been successful in getting jobs there and figuring out the expectations of the institution. Some of them will have a web presence, and some of those folks will likely have a CV of their own posted. If those CVs have information about religious background, then looking at half a dozen or so will give you a good idea about the sort of things that people at the institution think "religious background" should look like on a CV.
In particular, I would suggest looking for the CVs of people who have been there for a range of about 3-10 years. If they've been there for at least a few years, they're unlikely to be a misfit who would be a bad model for you to use. If it's within the last decade, then it's more likely to reflect the current practices, as opposed to somebody hired long ago who may or may not have been hired under different institutional cultural expectations.
Addendum: after writing this, I noticed a comment by the OP that none of the current faculty include this material in their online CV. This makes the requirement all the stranger, and based on that I would recommend just straight up asking the level of depth that is desired, proposing a couple of potential levels that you'd readily know how to give, e.g., "list of churches I've attended" vs. "paragraph explanation of the role of faith in my life."
I think they are asking about membership. If you are a member of a religious organization, add that as a line to your CV.
Member, First Church of College Town, State, Country.
If you hold some sort of leadership role in the religious organization, such as Elder or Board Member, that might also be listed in the CV.
Edit: This assumes your field of research is not religion.
I suggest that you read the web site of the college to see what they say about themselves and their expectations. I know that some demand that faculty follow the same principles that the college associates itself with. In this case, if you don't adhere to their beliefs it isn't really worth applying.
Others are much more tolerant of the views of others. At the extreme it might even be that diversity in the views of faculty is welcomed. The college may have a clear "mission" but not demand that everyone view that in the same way.
But, you will learn a lot, especially in the extreme cases from their web site. Some are very clear about expectations.
If they seem to be less stringent in their demands, then it may not matter much what you say or whether you say anything at all. But, since they ask, I guess they have expectations.
They are asking about your social contact with Christianity, were you baptized, did some services in/for a church or related organization, and so on.
It also hints, what do you believe.
The least useful if you have nothing. Being connected to another, or maybe even historically antithetical denomination, is probably still positive.
Note, Christianity is valid even to those who do not believe it. I.e. your human values are much more important than your denomination, and discriminating people for being non-christian is no-go. They probably try to detect these, and not (only) your denomination.
In your case I would say this: "baptized as (denomination), not very diligent but practicing observer and believer" or some similar. This would be a short part at the end of my CV (roughly in the place of the personal things/interests).
That your application would be refused only because what you write here, that is very unlikely.