We explore how assuming that mass traces light in strong gravitational lensing models can lead to systematic errors in the predicted position of multiple images. Using a model based on the galaxy cluster MACS J0416 (z = 0.397) from the Hubble Frontier Fields, we split each galactic halo into a baryonic and dark matter component. We then shift the dark matter halo such that it no longer aligns with the baryonic halo and investigate how this affects the resulting position of multiple images. We find for physically motivated misalignments in dark halo position, ellipticity, position angle and density profile that multiple images can move on average by more than 0.2 arcsec with individual images moving greater than 1 arcsec. We finally estimate the full error induced by assuming that light traces mass and find that this assumption leads to an expected rms error of 0.5 arcsec, almost the entire error budget observed in the Frontier Fields. Given the large potential contribution from the assumption that light traces mass to the error budget in mass reconstructions, we predict that it should be possible to make a first significant detection and characterization of dark halo misalignments in the Hubble Frontier Fields with strong lensing. Finally, we find that it may be possible to detect similar to 1 kpc offsets between dark matter and baryons, the smoking gun for self-interacting dark matter, should the correct alignment of multiple images be observed.