Oxygen abundance measurements are important for understanding stellar structure and evolution. Measured in Cepheids, they further provide clues on the metallicity gradient and chemo-dynamical evolution in the Galaxy... However, most of the abundance analyses of Cepheids to date have been based on one-dimensional (1D) hydrostatic model atmospheres. Here, we test the validity of this approach for the key oxygen abundance diagnostic, the \ion{O}{I} $777\,\mathrm{nm}$~triplet lines. We carry out 2D non-LTE radiative transfer clculations across two different 2D radiation hydrodynamics simulations of Cepheid atmospheres, having stellar parameters of $T_\mathrm{eff}= 5600$ K, solar chemical compositions, and $\log\,g= 1.5$ and $2.0$, corresponding to pulsation periods of 9 and 3 days, respectively. We find that the 2D non-LTE versus 1D LTE abundance differences range from $-1.0$~dex to $-0.25$~dex depending on pulsational phase. The 2D non-LTE versus 1D non-LTE abundance differences range from $-0.2$~dex to $0.8$~dex. The abundance differences are smallest when the Cepheid atmospheres are closest to hydrostatic equilibrium, corresponding to phases of around $0.3$ to $0.8$, and we recommend these phases for observers deriving the oxygen abundance from \ion{O}{I} $777\,\mathrm{nm}$ triplet with 1D hydrostatic models. (read more)