Rubber concrete (RC) is a new type of concrete that is currently receiving a lot of attention, solving serious pollution problems by grinding waste tires into granules and adding them to concrete. However, rubber concrete has deficiencies in mechanics and durability, and has been reinforced by adding fibers in many studies. In this study, the mechanical and durability properties of rubber concrete with added polypropylene and basalt fibers (PBRC) were investigated in a series of experiments including apparent morphology, mass, static compressive and tensile tests, ultrasonic non-destructive testing, and scanning electron microscope (SEM) tests under coupled environments of sulfate attack and freeze–thaw. The results showed that the mass loss rate of RC and PBRC gradually increased with the number of freeze–thaw cycles, with more pits and cement paste peeling from the specimen surface. Moreover, the compressive and splitting tensile strengths of RC and PBRC groups exhibited distinct trends, with the former group showing a lower residual strength relative to the latter. The residual compressive strength of the RC group was only 69.4% after 160 freeze–thaw cycles in 5% MgSO4solution. However, it is worth noting that the addition of too many fibers also had a negative effect on the strength of the rubber concrete. Additionally, the scanning electron microscopy (SEM) results indicated that the fibers restricted the formation of microcracks in the microstructure and curtailed the brittleness of the concrete. This study can provide a valuable reference for the application of environmentally friendly material fibers in recycled aggregate concrete.