We present the results of a search for galaxy alignments in 12 galaxy clusters at z > 0.5, a statistically complete subset of the very X-ray luminous clusters from the MAssive Cluster Survey (MACS). Using high-quality images taken with the Hubble Space Telescope (HST) that render measurement errors negligible, we find no radial galaxy alignments within 500 kpc of the cluster centres for a sample of 545 spectroscopically confirmed cluster members. A mild but statistically insignificant trend favouring radial alignments is observed within a radius of 200 kpc and traced to galaxies on the cluster red sequence. Our results for massive clusters at z > 0.5 are in stark contrast to the findings of previous studies which find highly significant radial alignments of galaxies in nearby clusters at z∼ 0.1 out to at least half the virial radius using imaging data from the Sloan Digital Sky Survey (SDSS). The discrepancy becomes even more startling if radial alignment becomes more prevalent at decreasing cluster-centric distance, as suggested by both ours and previous work. We investigate and discuss potential causes for the disparity between our findings based on HST images of clusters at z > 0.5 and those obtained using ground-based images of systems at z∼ 0.1. We conclude that the most likely explanation is either dramatic evolution with redshift (in the sense that radial alignments are less pronounced in dynamically younger systems) or the presence of systematic biases in the analysis of SDSS imaging data that cause at least partly spurious alignment signals.