ABSTRACT We present and study a large suite of high-resolution cosmological zoom-in simulations, using the FIRE-2 treatment of mechanical and radiative feedback from massive stars, together with explicit treatment of magnetic fields, anisotropic conduction and viscosity (accounting for saturation and limitation by plasma instabilities at high β), and cosmic rays (CRs) injected in supernovae shocks (including anisotropic diffusion, streaming, adiabatic, hadronic and Coulomb losses). We survey systems from ultrafaint dwarf ($M_{* }∼ 10^{4}\, \mathrm{M}_{⊙ }$, $M_{\rm halo}∼ 10^{9}\, \mathrm{M}_{⊙ }$) through Milky Way/Local Group (MW/LG) masses, systematically vary uncertain CR parameters (e.g. the diffusion coefficient κ and streaming velocity), and study a broad ensemble of galaxy properties [masses, star formation (SF) histories, mass profiles, phase structure, morphologies, etc.]. We confirm previous conclusions that magnetic fields, conduction, and viscosity on resolved ($\gtrsim 1\,$ pc) scales have only small effects on bulk galaxy properties. CRs have relatively weak effects on all galaxy properties studied in dwarfs ($M_{* } ≪ 10^{10}\, \mathrm{M}_{⊙ }$, $M_{\rm halo} \lesssim 10^{11}\, \mathrm{M}_{⊙ }$), or at high redshifts (z ≳ 1–2), for any physically reasonable parameters. However, at higher masses ($M_{\rm halo} \gtrsim 10^{11}\, \mathrm{M}_{⊙ }$) and z ≲ 1–2, CRs can suppress SF and stellar masses by factors ∼2–4, given reasonable injection efficiencies and relatively high effective diffusion coefficients $κ \gtrsim 3\times 10^{29}\, {\rm cm^{2}\, s^{-1}}$. At lower κ, CRs take too long to escape dense star-forming gas and lose their energy to collisional hadronic losses, producing negligible effects on galaxies and violating empirical constraints from spallation and γ-ray emission. At much higher κ CRs escape too efficiently to have appreciable effects even in the CGM. But around $κ ∼ 3\times 10^{29}\, {\rm cm^{2}\, s^{-1}}$, CRs escape the galaxy and build up a CR-pressure-dominated halo which maintains approximate virial equilibrium and supports relatively dense, cool (T ≪ 106 K) gas that would otherwise rain on to the galaxy. CR ‘heating’ (from collisional and streaming losses) is never dominant.