I've seen the WP page. If that's what FP is, then I think that means that either

  * think Lisps and Schemes aren't true FP, or
  * think that Lisps and Schemes avoid mutable state
Which one of those is your belief? I'm not a serious user of any allegedly-FP language, so maybe I misunderstand the history of FP. Note that I concede that Lisp seems to be less obsessed with mutating state than most procedural languages, but I think saying that it "avoids" it is an overreach.

Of course, some people could claim that "old" FP languages like Lisp and Scheme aren't truly FP.

As for your definition of OO, I think the word that describes abstraction across various instance-types is "polymorphism". That's when code can be written that handles multiple types, either because the typing system allows it, or because the typing system is so flexible that it fails to forbid it. Functional code is usually highly polymorphic, whether it's an aggressively static type system (Haskell with type classes) or an aggressively late-binding dynamic type system (typical Lisp, before anyone bothered to invent the phrase "duck typing").

Again, the central concept of OO, at least according to Alan Kay (the inventor/definer of the term), who said in 2003 (later than other definitions of his I could find) "OOP to me means only messaging, local retention and protection and hiding of state-process, and extreme late-binding of all things." I think it's pretty clear that statefulness is pretty essential to that definition.

http://userpage.fu-berlin.de/~ram/pub/pub_jf47ht81Ht/doc_kay...