Our covers are a mix of very course heavy duty fabric (like the stuff found in hotel
furnishings) and vinyl. They were absolutely filthy. So bad in fact the wife wanted to throw them away and start again with new ones.
We took the covers off the seats and cleaned them by a combination of soaking and washing
machine. It took three soaking / washing cycles to get them really clean again. The amount of dirt that came out of them was amazing!
No Ill effects resulted, but I guess it is material dependent.