Why isn't there a problem with washing your skin with water after dilute sulfuric acid gets on it?
Dilute sulphuric acid has already undergone the reaction!
The hydration reaction occurring when water is added to concentrated sulphuric acid is indeed exothermic, and the concentrated acid is fairly viscous. It means that if you get conc sulphuric acid on your skin and then run water over it, you create an isolated area where high temperatures are created, which can cause burns.
Dilute sulphuric acid, on the other hand, has already been hydrated.
Therefore washing this off your skin with water is simply diluting the dilute acid even more, so there is no danger.
Remember than there is a difference between concentrated sulphuric acid, which is predominantly (~96%)