Sadly, one reason for using the "Christian" factor in advertising help with handling debt would be "deception". Wherever there are dishonest people they usually have a very keen eye on how to gain your trust which they then violate. Some people are more likely to put their trust in a company who sets itself apart as being a Christian-based entity.
Hopefully that is the exception but it would be wise to scrutinize these agencies just as you would any other to be sure they are going to help and not hurt you.