For SSRs, when on, the reversed MOSFET's channel shunts its body diode so no significant current flows through the diode. When off, the normally-biassed MOSFET blocks current through the body diode of the reversed one.
However, in high power MOSFET H-bridges that have a Hi-Z state (where both the upper and the lower MOSFETs on one or both sides of it turn off simultaneously), it can be a problem. This is usually associated with letting a motor load free-wheel (coast). If the mechanical load can cause the motor to over-run faster than its normal maximum speed, that can cause uncontrolled conduction through the body diodes. If the body diodes don't have sufficient rating and you can't modify the system to eliminate the Hi-Z state, shunt them with suitably rated Schottky diodes, which will divert current from the body diodes.