In it's simplest terms, functional programming is programming without side-effects. Functions take inputs and produce outputs, but the inputs are not modifed. Crudely, pass by value rather than pass by reference.

Traditionally, regex modify their targets in-place rather then producing a modified copy of the original. I don't think that there is any technical reason why a regex-like find & replace facility couldn't be implemented in the functional style. Except maybe efficency, but as many will express, that can be a double edged sword.