I think many good hearted folks like you have a similar experience, Once. After that they call for an ambulance and let the folks with the easy to clean vehicle and protective clothes do their thing.
I'm with you though on washing vs. throwing. Properly washed no reason why the clothes and rags aren't reusable. I'd pay very close attention to seams and tight places in the vehicle though. Amazing where all the slop gets to. It gets harder to remove the longer it is in place.