Does the brain optimize itself for storage and transmission of information and if so, how? The critical brain hypothesis is based in statistical physics and posits that the brain self-tunes its dynamics to a critical point or regime to maximize the repertoire of neuronal responses. Yet, the robustness of this regime, especially with respect to changes in the functional connectivity, remains an unsolved fundamental challenge. Here, we show that both scale-free neuronal dynamics and self-similar features of behavioral dynamics persist following significant changes in functional connectivity. Specifically, we find that the psychedelic compound ibogaine that is associated with an altered state of consciousness fundamentally alters the functional connectivity in the retrosplenial cortex of mice. Yet, the scale-free statistics of movement and of neuronal avalanches among behaviorally-related neurons remain largely unaltered. This indicates that the propagation of information within biological neural networks is robust to changes in functional organization of sub-populations of neurons, opening up a new perspective on how the adaptive nature of functional networks may lead to optimality of information transmission in the brain.