Context. Hard X-ray properties of beamed active galactic nuclei have been published in the 105-month Swift/BAT catalog, but there have not been any studies carried out so far on a well-defined, radio-selected sample of low-peaked blazars in the hard X-ray band. Aims. Using the statistically complete MOJAVE-1 sample, we aim to determine the hard X-ray properties of radio-selected blazars, including the enigmatic group of gamma-ray-faint blazars. Additionally, we aim to determine the contribution of radio-selected low-peaked blazars to the diffuse cosmic X-ray background (CXB). Methods. We determined photon indices, fluxes, and luminosities in the range of 20 keV–100 keV of the X-ray spectra of blazars and other extragalactic jets from the MOJAVE-1 sample, derived from the 105-month Swift/BAT survey. We calculated log N–log S distributions and determined the luminosity functions. Results. The majority of the MOJAVE-1 blazars are found to be hard X-ray emitters albeit many at low count rates. The log N–log S distribution for the hard X-ray emission of radio-selected blazars is clearly non-Euclidean, in contrast to the radio flux density distribution. Approximately 0.2% of the CXB in the 20 keV–100 keV band can be resolved into MOJAVE-1 blazars. Conclusions. The peculiar log N–log S distribution disparity might be attributed to different evolutionary paths in the X-ray and radio bands, as tested by luminosity-function modeling. X-ray variability can be ruled out as the dominant contributor. Low-peaked blazars constitute an intrinsically different source population in terms of CXB contribution compared to similar studies of X-ray-selected blazars. The hard X-ray flux and spectral index can serve as a good proxy for the gamma-ray detection probability of individual sources. Future observations combining deep X-ray survey, for example, with eROSITA, and targeted gamma-ray observations with CTA can benefit strongly from the tight connection between these high-energy bands for the different blazar sub-classes.