  Type Ia supernovae play a critical role in stellar feedback and elemental
enrichment in galaxies. Recent transient surveys like the All-Sky Automated
Survey for Supernova (ASAS-SN) and the Dark Energy Survey (DES) find that the
specific Ia rate at z ~ 0 may be ~ 15-50 times higher in lower-mass galaxies
than at Milky Way-mass. Independently, Milky Way observations show that the
close-binary fraction of solar-type stars is higher at lower metallicity.
Motivated by these observations, we use the FIRE-2 cosmological zoom-in
simulations to explore the impact of varying Ia rate models, including
metallicity dependence, on galaxies across a range of stellar masses: 10^7 Msun
- 10^{11} Msun. First, we benchmark our simulated star-formation histories
(SFHs) against observations. We show that assumed SFHs and stellar mass
functions play a major role in determining the degree of tension between
observations and metallicity-independent Ia rate models, and potentially cause
ASAS-SN and DES observations to be much more consistent with each other than
might naively appear. Models in which the Ia rate increases with decreasing
metallicity (as ~ Z^{-0.5} to Z^{-1}) provide significantly better agreement
with observations. Encouragingly, these increases in Ia rate (> 10 times in
low-mass galaxies) do not significantly impact galaxy stellar masses and
morphologies: effective radii, axis ratios, and v/sigma remain largely
unaffected except for our most extreme rate models. We explore implications for
both [Fe/H] and [alpha/Fe] enrichment: metallicity-dependent Ia rate models can
improve agreement with observed stellar mass-metallicity relations in low-mass
galaxies. Our results demonstrate that a wide range of metallicity-dependent Ia
models are viable for galaxy formation and motivate future work in this area.
