I never had a washing machine in my home till I moved to the UK, so I'm not used to anything different.
I also don't understand why the clean clothes would get covered with food. Food is in the fridge, in cupboards, in boxes, cans, jars, etc. It's not flying all over the place.
If you are cooking or preparing food while the washing machine is on, the door of the washing machine will be closed.
You can take the clothes somewhere else to sort them or fold them.