UPDATE: Anon731A makes a very good point: "Please don't assume that if a college has a religious affiliation, that a statement of faith is required."
I asked an old friend of mine about how they successfully applied for a tenure-track position at a religiously-affiliated institution. They generously shared their full application for the position, which included their statement of faith (which, I presume, was required for the application.) Amusingly, they admitted out how to write this portion by Googling "statement of faith."
I won't quote from it directly to preserve its privacy, but it's a medium-length document, approximately 900 words. As one might imagine, it's a very personal document, talking about their childhood religious upbringing, formative spiritual experiences during adolescence, their faith practice during their undergraduate, graduate and postdoctoral times as well as their current faith life. There is a short paragraph on how their ideal spiritual life might mesh well with the potential institution's vision for Christian community. Finally, there is a short (one sentence per line) reflection on the Apostle's Creed.
I recognize that this is just one example - I hope this helps folks who are interested in applying for positions at religious institutions. Readers who are professors at church-based colleges and universities, any thoughts?