Trustees of pensions, university endowments and trust funds are facing renewed pressure to do social good while investing other people’s money. It isn’t only student activists but the United Nations and even BlackRock CEO Larry Fink who argue that environmental, social and governance investing, or ESG, will do good for the world while improving returns for beneficiaries. Thousands of investment managers have pledged to abide by a U.N.-sponsored statement of ESG principles.

Yet the zealous push for fiduciaries to embrace ESG...