Artificial spin ice (ASI) systems have emerged as promising hosts for magnonic applications due to a correspondence between their magnetic configuration and spin dynamics. Though it has been demonstrated that spin-wave spectra are influenced by the ASI microstate the precise nature of this relationship has remained unclear. Recent advances in controlling the magnetic configuration of ASI make harnessing the interplay between spin dynamics and the microstate achievable. This could allow diverse applications including reconfigurable magnonic crystals and programmable microwave filters. However, extracting any novel functionality requires a full understanding of the underlying spin-wave/microstate interaction. Here, we present a systematic analysis of how the microstate of a honeycomb ASI system affects its spin-wave spectrum through micromagnetic simulations. We find the spectrum to be highly tunable via the magnetic microstate, allowing the (de)activation of spin-wave modes and band-gap tuning via magnetic reversal of individual nanoislands. Symmetries of ASI systems and the chirality of “monopole” defects are found to play important roles in determining the high-frequency magnetic response.