The rapid deployment of AI-powered collaborative robots (cobots) in industrial manufacturing settings has created a growing mismatch between technological capability and public willingness to accept these systems. Despite significant technical advances, robot-related fear, cultural resistance, and poor science communication continue to hinder adoption across major industrial economies. This review synthesises evidence from 86 peer-reviewed sources (2016–2025) across four areas: media framing and public narratives; technology acceptance frameworks (TAM, HRCAM, and the Uncanny Valley effect); cross-national empirical findings from Germany, Japan, China, South Korea, the USA, and the UK; and practical science communication strategies. We find that robot-related fear affects 29–52% of national populations depending on cultural and institutional context; that hands-on and immersive exposure consistently outperforms informational campaigns in reducing anxiety; that existing acceptance models underestimate emotional, safety, and psychological barriers to cobot adoption; and that no single communication strategy succeeds uniformly across cultural settings. Key findings indicate that worker participation in deployment processes, transparent employment communication, explainable AI interfaces, and culturally adapted messaging each independently improve acceptance outcomes. The review further demonstrates that media framing—predominantly dystopian in Western contexts—shapes worker attitudes prior to any formal introduction programme. Four research gaps are identified: the absence of industrial-context science communication studies, underrepresentation of the Global South, the lack of longitudinal data, and underdeveloped use of immersive technologies. Directions for future work are proposed.