Our knowledge of the initial conditions of terrestrial planet formation is mainly based on the study of protoplanetary disks around nearby isolated low-mass stars. However, most young stars and therefore planetary systems form in high-mass star-forming regions and are exposed to ultraviolet radiation, affecting the protoplanetary disk. These regions are located at large distances and only now with JWST has it become accessible to study the inner disks surrounding young stars. We present the eXtreme UV Environments (XUE) program, which provides the first detailed characterization of the physical and chemical properties of the inner disks around young intermediate-mass (1-4M_{sun}_) stars exposed to external irradiation from nearby massive stars. We present high-signal-to-noise MIRI-MRS spectroscopy of 12 disks located in three subclusters of the high-mass star-forming region NGC 6357 (d~1690pc). Based on their mid-infrared spectral energy distribution, we classified the XUE sources into Group I and II based on the Meeus scheme. We analyzed their molecular emission features, and compared their spectral indices and 10um silicate emission profiles to the ones of nearby Herbig and intermediate T Tauri (IMTT) disks. The XUE program provides the first detailed characterization of the rich molecular inventory in IMTT disks, including water, CO, CO_2_, HCN, and C_2_H_2_. In the XUE sample, the detected emission likely originates from within 10au, although this inner disk origin may not be typical for all externally irradiated disks. Despite being more massive, the XUE stars host disks with a molecular richness comparable to isolated T Tauri systems. The spectral indices are also consistent with similar-mass stars in nearby regions. The 10um silicate features in the XUE sample exhibit lower F11.3/F9.8 ratios at a given Fpeak, suggesting that the disk surfaces may be dominated by smaller grains compared to nearby disks. However, uncertainties in extinction prevent us from drawing firm conclusions about their inner disk properties. The majority of disks display water emission from the inner disk, suggesting that even in these extreme environments rocky planets can form in the presence of water. Only one object shows PAH emission, contrasting with the higher PAH detection rates in IMTT surveys from lower-UV environments. The absence of strong line fluxes and other irradiation signatures suggests that the XUE disks have been truncated by external UV photons. However, this truncation does not appear to significantly impact the chemical richness of their inner regions. These findings indicate that even in extreme environments, IMTT disks can retain the ingredients necessary for rocky planet formation, comparable to the ones of lower-mass T Tauri disks in low-mass star-forming regions.