Base station antennas include a RET actuator, a plurality of phase shifters and a plurality of mechanical linkages, where each mechanical linkage is connected between the RET actuator and a respective one or more of the phase shifters. The RET actuator includes a drive element, a rotatable element and a mechanical linkage selection system that is configured to move a selected one of the mechanical linkages into engagement with the drive element. The drive element is configured to move linearly in response to rotation of the rotatable element to move the selected one of the mechanical linkages.