The high concentrations derived for several strong-lensing clusters present a major inconsistency between theoretical Λ cold dark matter (ΛCDM) expectations and measurements. Triaxiality and orientation biases might be at the origin of this disagreement, as clusters elongated along the line of sight would have a relatively higher projected mass density, boosting the resulting lensing properties. Analyses of statistical samples can probe further these effects and crucially reduce biases. In this work we perform a fully triaxial strong-lensing analysis of the 12 Massive Cluster Survey (MACS) clusters at z > 0.5, a complete X-ray-selected sample, and fully account for the impact of the intrinsic 3D shapes on their strong-lensing properties. We first construct strong-lensing mass models for each cluster based on multiple images, and fit projected ellipsoidal Navarro–Frenk–White haloes with arbitrary orientations to each mass distribution. We then invert the measured surface mass densities using Bayesian statistics. Although the Einstein radii of this sample are significantly larger than those predicted by ΛCDM, here we find that the mass–concentration relation is in full agreement with results from N-body simulations. The z > 0.5 MACS clusters suffer from a moderate form of the orientation bias as may be expected for X-ray-selected samples. Being mostly unrelaxed, at a relatively high redshift, with high X-ray luminosity and notable substructures, these clusters may lie outside the standard concentration–Einstein radius relation. Our results remark the importance of triaxiality and properly selected samples for understanding galaxy clusters properties and suggest that for higher-z, unrelaxed low-concentration clusters form a different class of prominent strong gravitational lenses. Arc redshift confirmation and weak-lensing data in the outer region are needed to further refine our analysis.