An effective field theory framework, the Standard-Model Extension, is used to investigate the existence of Lorentz and CPT-violating effects during gravitational wave propagation. We implement a modified equation for the dispersion of gravitational waves, that includes isotropic, anisotropic and birefringent dispersion. Using the LIGO-Virgo-KAGRA algorithm library suite, we perform a joint Bayesian inference of the source parameters and coefficients for spacetime symmetry breaking. From a sample of 45 high confidence events selected in the GWTC-3 catalog, we obtain a maximal bound of 3.19 × 10 −15 m at 90% CI for the isotropic coefficient k(5) (V )00 when assuming the anisotropic coefficients to be zero. The combined measurement of all the dispersion parameters yields limits on the order of 10 −13 m for the 16 k(5) (V )ij coefficients. We study the robustness of our inference by comparing the constraints obtained with different waveform models, and find that a lack of physics in the simulated waveform may appear as spacetime symmetry breaking-induced dispersion for a subset of events.