Reputation would not be on you, as a physical human being. It would be on the GPG public key.
Right, I get that. So would the reputation of your GPG key be akin to a credit rating of sorts? Would the CU use the key's reputation as a means of determining the eligibility for a loan? In that case, every new customer would essentially start with zero reputation since there would be no 'credit history' for the key.
Reputation would not be anything formal. For each public keys, there would be some data about successful or failed loans. It's up to you to use this data and give a credit rating.
And yes, every one would start from a "zero reputation".
By the way, such a system has already started on #bitcoin-otc.