We combine the latest spectrally stacked data of 21-cm emission from the Arecibo Legacy Fast ALFA survey with an updated version of the DARK SAGE semi-analytic model to investigate the relative contributions of secular and environmental astrophysical processes on shaping the HI fractions and quiescence of galaxies in the local Universe. We calibrate the model to match the observed mean HI fraction of all galaxies as a function of stellar mass. Without consideration of stellar feedback, disc instabilities and active galactic nuclei, we show how the slope and normalization of this relation would change significantly. We find DARK SAGE can reproduce the relative impact that halo mass is observed to have on satellites' HI fractions and quiescent fraction. However, the model satellites are systematically gas-poor. We discuss how this could be affected by satellite-central cross-contamination from the group-finding algorithm applied to the observed galaxies, but that it is not the full story. From our results, we suggest the anticorrelation between satellites' HI fractions and host halo mass, seen at fixed stellar mass and fixed specific star formation rate, can be attributed almost entirely to ram-pressure stripping of cold gas. Meanwhile, stripping of hot gas from around the satellites drives the correlation of quiescent fraction with halo mass at fixed stellar mass. Further detail in the modelling of galaxy discs' centres is required to solidify this result, however. We contextualize our results with those from other semi-analytic models and hydrodynamic simulations.