Highly reddened type Ia supernovae (SNe Ia) with low total-to-selective visual extinction ratio values, RV, also show peculiar linear polarization wavelength dependencies with peak polarizations at short wavelengths ({lambda}_max_<~0.4um). It is not clear why sightlines to SNe Ia display such different continuum polarization profiles from interstellar sightlines in the Milky Way with similar RV values. We investigate polarization profiles of a sample of Galactic stars with low RV values, along anomalous extinction sightlines, with the aim to find similarities to the polarization profiles that we observe in SN Ia sightlines. We undertook spectropolarimetry of 14 stars, used archival data for 3 additional stars, and ran dust extinction and polarization simulations (by adopting the picket-fence alignment model) to infer a simple dust model (size distribution, alignment) that can reproduce the observed extinction and polarization curves. Our sample of Galactic stars with low RV values and anomalous extinction sightlines displays normal polarization profiles with an average {lambda}_max_~0.53um, and is consistent within 3{sigma} to a larger coherent sample of Galactic stars from the literature. Despite the low RV values of dust toward the stars in our sample, the polarization curves do not show any similarity to the continuum polarization curves observed toward SNe Ia with low RV values. There is a correlation between the best-fit Serkowski parameters K and {lambda}_max_, but we did not find any significant correlation between RV and {lambda}_max_. Our simulations show that the K-{lambda}_max_ relationship is an intrinsic property of polarization. Furthermore, we have shown that in order to reproduce polarization curves with normal {lambda}_max_ and low RV values, a population of large (a >=0.1um) interstellar silicate grains must be contained in the dust composition.