We present a photometric and spectroscopic study of stellar populations in the X-ray–luminous cluster of galaxies RX J0142.0+2131 at z = 0.280. This paper analyzes the results of high signal-to-noise ratio spectroscopy, as well as g'-, r'-, and i'-band imaging, using the Gemini Multi-Object Spectrograph on Gemini North. Of 43 spectroscopic targets, we find 30 cluster members over a range in color. Central velocity dispersions and absorption-line strengths for lines in the range 3700 Å λ_rest 5800 Å are derived for cluster members and are compared with a low-redshift sample of cluster galaxies and single stellar population (SSP) models. We use a combination of these indicators to estimate luminosity-weighted mean ages, metallicities ([M/H]), and α-element abundance ratios ([α/Fe]). RX J0142.0+2131 is a relatively poor cluster and lacks galaxies with high central velocity dispersions. Although the red sequence and the Faber-Jackson relation are consistent with pure passive evolution of the early-type population with a formation redshift of z_form 2, the strengths of the 4000 Å break and scaling relations between metal line indices and velocity dispersion reject this model with high significance. By inverting SSP models for the Hβ_G, Mg b, and Fe line indices, we calculate that, at a given velocity dispersion and metallicity, galaxies in RX J0142.0+2131 have luminosity-weighted mean ages 0.14 ± 0.07 dex older than the low-redshift sample. We also find that [α/Fe] in stellar populations in RX J0142.0+2131 is 0.14 ± 0.03 greater than at low redshift. All scaling relations are consistent with these estimated offsets. We speculate that the older luminosity-weighted mean ages and [α/Fe] enhancement can be brought about by a rapidly curtailed burst of star formation in RX J0142.0+2131, such as may be experienced in a cluster-cluster merger. We note that the cluster's velocity dispersion, 1278 ± 134 km s^-1, is larger than expected from both its X-ray luminosity and richness. However, the velocity distribution of galaxies in RX J0142.0+2131 is consistent with being drawn from a Gaussian distribution, and no sign of substructure is found. We conclude that stellar populations in RX J0142.0+2131 cannot evolve into stellar populations similar to those seen in our low-redshift sample through passive evolution. This study provides further evidence that a more complex model, possibly involving ongoing or intermittent star formation and galaxy mergers, is required to describe the evolution of cluster galaxies.