Possibly Asbestos Contaminated Washer! What do I do?
I wouldn't worry so much about it. Wipe it down as best you can and then run a few empty cycles to flush the machine. The wastewater goes... well assuming you are in a relatively modern area with relatively modern infrastructure... to a treatment plant along with myriad other nasty stuff.
While it is true that any exposure to friable asbestos should be avoided, data shows that the real risk is chronic (i.e. prolonged) exposure as would occur in industrial or job-specific exposure scenarios.