<p>A modified noisy voter model is considered on time-varying scale-free networks with different degrees of assortativity. Within the model, the avalanche-like dynamics of the threshold variables (stress) assigned to voters leads to changes in their binary states (opinions). The system response to an avalanche is defined as the change in the system average opinion caused by this perturbation. It is shown analytically and numerically that increasing network assortativity leads to a disordering of the system dynamics. For systems of finite size, the dynamics changes from switching between consensuses to a state where opposing opinions coexist and the system average opinion is close to zero. At the same time, the increasing assortativity stabilizes the system response. This stabilization manifests itself in a decrease in both the maximum value of the response magnitude and the probability of large responses.</p>