Conserved Currents are Not Anomaly-Safe

New vector bosons that are coupled to conserved currents in the Standard Model exhibit enhanced rates below the electroweak scale from anomalous triangle amplitudes, leading to (energy/vector mass)^2 enhancements to rare Z decays and flavor-changing meson decays into the longitudinally polarized vector boson. In the case of a vector boson gauging U(1)_B-L, the mass gap between the top quark and the remaining SM fermions leads to (energy/vector mass)^2 enhancements for processes with momentum transfer below the top mass. In addition, we examine the case of an intergenerational U(1)_B_3 - L_2 that has been proposed to resolve the (g-2)_μ anomaly with an MeV scale DM candidate, and we find that these enhanced processes constrain the entire parameter space.