Agree. Probably best to handwash first, or at least soak in a bucket before putting in the washing machine. I know that stuff seems really fine, but with some manual agitation, you should be able to get a good amount of the stuff out of the fibers.
The dirt effects are mostly just pigment and maybe a little filler. There isn't anything in them to cause the pigments to set or stain. It should wash out just fine. It's formulated for the purpose. It's used to make stage-actors look dirty, and this wouldn't be of much use if it stained clothes so they couldn't be worn for repeat performances.