First, while it's true that the German "Schulden" is related to "Schuld", it's also true that one of the definitions of "debt" is "sin". I don't know if many anthropologists really have wasted much time thinking about this one, but it seems pretty irrelevant to me.
Second, the German banking system is actually very modern. While the Americans and British are still sending cheques through the post, Germans are regularly paying by direct debit and standing order, as a matter of course.
Third, I think a point that may be missing is that Germans might be suspicious of credit card payments as they leave records which can be inspected by government agencies. It's bad enough that they might be able to find out how much rent you pay and how much electricity you use, but they really don't need to know exactly which bar you got drunk in last night. I don't know if anyone's done any serious study into this one, but it is very noticeable that Germans are particularly concerned about their privacy.