We present uniformly measured stellar metallicities of 463 stars in 13 Milky Way (MW) ultra-faint dwarf galaxies (UFDs; M-V = -7.1 to -0.8) using narrowband CaHK (F395N) imaging taken with the Hubble Space Telescope. This represents the largest homogeneous set of stellar metallicities in UFDs, increasing the number of metallicities in these 13 galaxies by a factor of 5 and doubling the number of metallicities in all known MW UFDs. We provide the first well-populated MDFs for all galaxies in this sample, with <[Fe/H]> ranging from -3.0 to -2.0 dex, and sigma([Fe/H]) ranging from 0.3-0.7 dex. We find a nearly constant [Fe/H]similar to -2.6 over 3 decades in luminosity (similar to 10(2)-10(5)L(circle dot)), suggesting that the mass-metallicity relationship does not hold for such faint systems. We find a larger fraction (24%) of extremely metal-poor ([Fe/H]< -3) stars across our sample compared to the literature (14%), but note that uncertainties in our most metal-poor measurements make this an upper limit. We find 19% of stars in our UFD sample to be metal-rich ([Fe/H] > -2), consistent with the sum of literature spectroscopic studies. MW UFDs are known to be predominantly >13 Gyr old, meaning that all stars in our sample are truly ancient, unlike metal-poor stars in the MW, which have a range of possible ages. Our UFD metallicities are not well matched to known streams in the MW, providing further evidence that known MW substructures are not related to UFDs. We include a catalog of our stars to encourage community follow-up studies, including priority targets for ELT-era observations.