I have a 1930s RPPC that has some back crap on it (probably from scrap book mounting) that I am in the process of removing so I can read the card back.
IMO there is nothing wrong with anything that a good conservator would do to a card--removing paper bits, deacidifying, removing a stain--so long as it doesn't damage the card itself.
Love the car analogy, BTW but I bet if I washed mine parts would fall off--the bird crap is all that's holding them on