Both borrowers and lenders can be socially responsible (SR). Ethical banks commit to financing only ethical projects, which have social profitability but lower expected revenues than standard projects. Instead, no credible commitment exists for SR borrowers. The matching between SR borrowers and ethical banks reduces the frictions caused by moral hazard. However, when the type of the borrowers is not observable, then standard borrowers have incentives to invest in ethical projects pretending to be SR. We show that the separation of borrowers entails costs that are paid by SR entrepreneurs but are relatively low because standard lenders offer an outside option that relaxes the self-selection constraint of the borrowers. Technically, we solve a Contract Proposal Game where informed principals (borrowers) offer different menus of contracts to heterogeneous agents (banks). We show that market segmentation improves efficiency and solves the problem of multiplicity of equilibria in Contract Proposal Games.