Blowing Dust Can Be a Problem for Valley Commuters
Blowing dust can be a problem at any time of the year, not just during monsoon season. The best advice from ADOT is to avoid stopping. Instead commuters should move to the side of the road and turn off their lights. Don't stop for debris like tumbleweeds which are fairly harmless to a vehicle. When pulled over, use the emergency brake and remove foot from the brake.
Here's a useful Dust Storm Fact Sheet from ADOT and another on Storm Safety.
AZFamily.com offers a simple video with some good advice for commuters.