Fridge has a filter so you don't need to worry about particulate in the water if anyone is suggesting that it might be an issue with the grade of pipe used for b the washer vs drinking water pipes. I've never heard of there being a difference...but I'm sure 94 ppl will point it out if this is indeed a thing.

The other reason it's not an issue is because your washer doesn't really rely on water pressure to perform. It just needs to flow and fill the drum in the washer.