We examine the chemical properties of five cosmological hydrodynamical simulations of an M33-like disc galaxy which have been shown previously to be consistent with the morphological characteristics and bulk scaling relations expected of late-type spirals. These simulations are part of the Making Galaxies in a Cosmological Context Project, in which stellar feedback is tuned to match the stellar mass–halo mass relationship. Each realization employed identical initial conditions and assembly histories, but differed from one another in their underlying baryonic physics prescriptions, including (a) the efficiency with which each supernova energy couples to the surrounding interstellar medium, (b) the impact of feedback associated with massive star radiation pressure, (c) the role of the minimum shut-off time for radiative cooling of Type II supernovae remnants, (d) the treatment of metal diffusion and (e) varying the initial mass function. Our analysis focusses on the resulting stellar metallicity distribution functions (MDFs) in each simulated (analogous) ‘solar neighbourhood’ (2–3 disc scalelengths from the galactic centre) and central ‘bulge’ region. We compare and contrast the simulated MDFs’ skewness, kurtosis and dispersion (inter-quartile, inter-decile, inter-centile and inter-tenth-percentile regions) with that of the empirical solar neighbourhood MDF and Local Group dwarf galxies. We find that the MDFs of the simulated discs are more negatively skewed, with higher kurtosis, than those observed locally in the Milky Way and Local Group dwarfs. We can trace this difference to the simulations’ very tight and correlated age–metallicity relations (compared with that of the Milky Way's solar neighbourhood), suggesting that these relations within ‘dwarf’ discs might be steeper than in L★ discs (consistent with the simulations’ star formation histories and extant empirical data), and/or the degree of stellar orbital redistribution and migration inferred locally has not been captured in their entirety, at the resolution of our simulations. The important role of metal diffusion in ameliorating the overproduction of extremely metal-poor stars is highlighted.