Nobody can answer that without knowing what the circut does and why there are two supplies in the first place.
Let me give you an example:
A motor turns and makes a conveyor belt move. At the end of the conveyor there is a light beam sensor that turns the motor off when an object breaks the beam. Suppose the sensor is operated by the DC supply (as would be normal) but the motor is controlled by the AC supply. If you switch the DC on first, the system can immediately check if the beam is broken already or if it is safe to turn the motor on. If the AC was turned on first, the motor might move and leave a pile of broken items on the floor as they drop off the end because the sensor wasn't working.
Brian.