I wouldn't wash the fabric on the car seat or stroller. Washing car seat fabric is a huge pain, as you'll probably find out at some point after a major spit-up or blowout. You pretty much have to take the entire car seat apart. Stroller fabric isn't as bad, but still bad, and it will fade depending on the type of stroller you have. Pre-washing infant clothing is to prevent packing or dying chemicals from coming in contact with their delicate skin, but I wouldn't worry about it with the car seat or stroller.
Baby Soap Shampoo Wash

Hi there, I would hand wash it. Sunlight soap is the best and give it a good soak and rub with your hands and the marks should come out. DON'T put it in the washing machine, so many websites say just machine wash but I don't recommend it. I saw someone trying to sell a second hand hood once and it had completely skewed out of shape. They don't take long to wash/ rinse until water clean and squeeze hard and dry in the shade. Don't put any cleaning substances/ upholstery cleaners on it, Sunlight soap is the all time favourite for this sort of thing and gets most marks out. If you don't know what Sunlight soap is then any pure soap or baby friendly detergent/ washing soap would do (any with a picture of a baby on it.