Extremist communities increasingly rely on social media to sustain and amplify divisive discourse. However, the relationship between their internal participation structures, audience engagement, and narrative expression remains underexplored. This study analyzes ten years of Facebook activity by hate groups related to the Israel-Palestine conflict, focusing on anti-Semitic and Islamophobic ideologies. Consistent with prior work, we find that higher participation centralization in online hate groups is associated with greater user engagement across hate ideologies, suggesting the role of key actors in sustaining group activity over time. Meanwhile, our narrative frame detection models--based on an eight-frame extremist taxonomy (e.g., dehumanization, violence justification)--reveal a clear contrast across hate ideologies: centralized Islamophobic groups employ more uniform messaging, while centralized anti-Semitic groups demonstrate greater framing diversity and topical breadth, potentially reflecting distinct historical trajectories and leader coordination patterns. Analysis of the inter-group network indicates that, although centralization and homophily are not clearly linked, ideological distinctions emerge: Islamophobic groups cluster tightly, whereas anti-Semitic groups remain more evenly connected. Overall, these findings clarify how participation structure may shape the dissemination pattern and resonance of extremist narratives online and provide a foundation for tailored strategies to disrupt or mitigate such discourse.