They can go straight in the fridge unwashed You’d just wash them right before you use them, always with hot water. What you don’t want to do is fridge them and then let them sit out, they’ll get condensation and the bacteria can move through the shell. I put all my eggs straight in the fridge every afternoon when I collect them, it extends their life.
Personally, I do wash the super grimy ones right way, when it’s muddy or when someone snuck a into the nestbox that I didn’t catch.