Despite AI's promise for addressing global challenges, empirical understanding of AI adoption in mission-driven organizations (MDOs) remains limited. While research emphasizes individual applications or ethical principles, little is known about how resource-constrained, values-driven organizations navigate AI integration across operations. We conducted thematic analysis of semi-structured interviews with 15 practitioners from environmental, humanitarian, and development organizations across the Global North and South contexts. Our analysis examines how MDOs currently deploy AI, what barriers constrain adoption, and how practitioners envision future integration. MDOs adopt AI selectively, with sophisticated deployment in content creation and data analysis while maintaining human oversight for mission-critical applications. When AI's efficiency benefits conflict with organizational values, decision-making stalls rather than negotiating trade-offs. This study contributes empirical evidence that AI adoption in MDOs should be understood as conditional rather than inevitable, proceeding only where it strengthens organizational sovereignty and mission integrity while preserving human-centered approaches essential to their missions.