Washing or peeling fruits and vegetables won’t protect you from systemic pesticides spread throughout the plant's tissues.
Systemic pesticides are in the plant, not on it. When we make the plant itself poisonous to predators, one has to wonder what (or who) else it’s poisoning.
A garden seed company recently sent us these seeds for a new sweet corn. The seeds were treated with Cruiser, which is thiamethoxam, a systemic neonicotinoid insecticide. They were also treated with four fungicides: azoxystrobin, carboxin, fludioxonil and mefenoxam!