L.P.
I never pay attention to the 'do not put in washing machine' labels.
My son's travel system was Graco, and said the same thing. Well, I washed the covers of the carseat and stroller several times in the washing machine, on the regular cycle, and they came out just fine. I would hang them to dry. No unraveling, no fading, no shrinking, nothing.
Hope this helps.