The integration of distributed energy resources (DERs) into contemporary energy communities (ECs) has revolutionized power systems, fostering sustainable and clean energy infrastructures. This paper focuses on the effective load-carrying capability (ELCC) to enhance grid resilience in the presence of DERs. We introduce an innovative network topology-based optimization framework that seamlessly integrates economic and resilience metrics within ECs while reducing carbon emissions. The Pareto front of non-dominated solutions for the proposed three-objective optimization problems is extracted, providing a comprehensive visualization of the trade-off between economic, resilience, and emission objectives, enabling informed decision-making. Analytical results, validated on the IEEE 33-bus test system, demonstrate the effectiveness of DER-based ELCC quantification in managing load supply during emergencies. Case studies show how the synergy between economic and resilience-based metrics significantly enhances grid resilience. The proposed framework has diverse applications, including enhancing grid adaptability to climate change, promoting sustainable energy integration, optimizing demand response strategies, and supporting the transition to a decarbonized energy community. This work addresses the challenges and opportunities in the evolving energy landscape, emphasizing the importance of our approach in achieving a cleaner and more resilient energy future.