On April 7th the Muon g-2 collaboration at FNAL presented its first measurement of the anomalous magnetic moment of the muon. The result is consistent with previous measurements, yielding an experimental world average larger than the Standard Model prediction by about 4.2 standard deviations. The very same day, a new lattice QCD evaluation of the hadronic vacuum polarization contributing to muon g-2 was published. The resulting (alternative) Standard Model prediction is good agreement with the data, suggesting that new physics particles coupled to muons are tightly constrained, notably below the GeV scale. I will present a new physics model consisting of scalar and pseudoscalar states whose one-loop contribution to muon g-2 is parametrically suppressed as a result of symmetry. This has important consequences for the ongoing program of direct searches of such particles.