The observed abundance of giant arcs produced by galaxy cluster lenses and the measured Einstein radii have presented a source of tension for Λ cold dark matter (ΛCDM), particularly at low redshifts (z ∼ 0.2). Previous cosmological tests for high-redshift clusters (z > 0.5) have suffered from small number statistics in the simulated sample and the implementation of baryonic physics is likely to affect the outcome. We analyse zoomed-in simulations of a fairly large sample of cluster-sized objects, with Mvir > 3 × 1014 h−1 M⊙, identified at z = 0.25 and 0.5, for a concordance ΛCDM cosmology. These simulations have been carried out by incrementally increasing the physics considered. We start with dark-matter-only simulations and then add gas hydrodynamics, with different treatments of baryonic processes: non-radiative cooling, radiative cooling with star formation and galactic winds powered by supernova explosions, and finally including the effect of active galactic nucleus (AGN) feedback. Our analysis of strong lensing properties is based on the computation of the cross-section for the formation of giant arcs and of the Einstein radii. We find that the addition of gas in non-radiative simulations does not change the strong lensing predictions significantly, but gas cooling and star formation together significantly increase the number of expected giant arcs and the Einstein radii, particularly for lower redshift clusters and lower source redshifts. Further inclusion of AGN feedback reduces the predicted strong lensing efficiencies such that the lensing probability distributions become closer to those obtained for simulations including only dark matter. Our results indicate that the inclusion of baryonic physics in simulations will not solve the arc-statistics problem at low redshifts, when the physical processes included provide a realistic description of cooling in the central regions of galaxy clusters. As outcomes of our analysis, we encourage the adoption of Einstein radii as a robust measure of strong lensing efficiency, and provide the ΛCDM predictions to be used for future comparisons with high-redshift cluster samples.