“When a symbol is crossed out,” she warns, “that’s your sign not to do that ... that means your garment should be hand-washed ...
You can certainly transfer some bacteria from meat to salad, for example, so it's a good idea to not only wash your hands before but also while you are preparing food, also after and of course ...
Even if you only use the gentle cycle in a washer, hand-washing is less harmful than the agitation and spinning forces in a washer. Some garments that have a "dry clean" label can be hand-washed.