Can soap reduce incidence of MRSA?

Yes.

MRSA can be prevented with standard hygiene practices of soap and water. If you have heard the advice wash your hands under water as warm as you can tolerate it and sing happy birthday to yourself while washing your hands vigorously under the water with soap. It should take about 20-30 seconds. This is also how they do the hospital inservice for Hand Washing technique. Using hand Sanitizers are not recommended for this because they are only designed to cover up and may be able to kill weaker bacteria. Proper handwashing will remove dirt and most harmful substances, dead skin, oils from the hands.

This advice is not concrete due to other factors that can make this change such as cuts on the hand, previously having MRSA, etc.