Getting mild electric shocks from tap water if washing machine is switched on
This sounds like a pretty dangerous situation. There are some things you could check.

A. Look into if the earth grounding connection at your house is  good solid connection without corrosion.

B. Try seeing if you get the same tingling effect when you run a different appliance plugged into the same outlet such as a blender or toaster.

C. Check if the outlets near your kitchen sink are protected with GFCI devices.