What best defines individuals who work together to advance their shared extremist ideas without an organizational structure?

The term that best defines individuals who collaborate to promote shared extremist ideas without a formal organizational structure is referred to as an extremist movement. This concept emphasizes the fluidity and decentralized nature of such groups, highlighting how individuals can unite around common beliefs or ideologies without needing a hierarchical organization.

Extremist movements are often characterized by grassroots mobilization, with participants engaging in activities that promote their views, often through informal networks or social interactions. This contrasts with the more structured and organized nature of a terrorist organization, which typically operates with clear leadership and defined strategies. Similarly, a radical group may imply a more organized faction, while an insurgency network generally denotes a group engaged in active resistance or rebellion against an established authority, often with a clear command structure.

Therefore, the definition of an extremist movement captures the essence of loosely connected individuals working toward a common cause, making it the best choice in this context.