Process executors should perceive responsible business process management within an enterprise. It is employees who primarily experience changes in daily operations. If they can connect these changes with their company’s purposeful and long-term orientation, we can speak of anchoring certain concepts in everyday practice. This paper aims to determine the nature of Polish enterprises’ activities in achieving ESG (Environmental, Social, Governance) goals in business processes, their connection with ESG strategy, and institutional pressure and legislative initiatives at the national and European Union levels. The presented survey research conducted among employees representing 547 Polish organizations indicates strong anchoring of ESG goals in business processes and simultaneously statistically significant relationships between strategic and process management. The perceived institutional pressure for ESG goal implementation and its actual impact on enterprise behavior have been confirmed in statistical tests. At the same time, an important research finding is identifying weak support from business environment institutions for sustainable development. The research results may provide knowledge to managers implementing ESG goals, BPMS software suppliers, and training service providers regarding managerial, resource, and technological support.