It all depends on the lens one chooses to view them. None of them are really "functional programming" in the truly modern sense, even F#. As more and more mainstream languages get pattern matching and algebraic data types (such as Python), feature lambdas and immutable values, then these languages converge. However, you don't really get the promises of functional programming such as guaranteed correct composition and easier reasoning/analysis, for that one needs at least purity and perhaps even totality. That carries the burden of proof, which means things get harder and perhaps too hard for some (e.g. the parent poster).
I am an avid functional programmer (it’s my default when working on solo projects) and I teach a PL class that covers the lambda calculus, LISP, etc. But the bulk of the course uses F#. I’ve been using F# regularly for the last 13 years.
It’s pretty easy to stick to pure F# if what you want is the pure functional programming experience. But what I like about it is its pragmatism, and this is a big reason why it’s the language I chose for the course. It is by-value, eagerly evaluated by default, and has an easy-to-learn idiomatic syntax. It has a large and well-behaved standard library, and you can use C#’s excellent standard library if you need additional things (e.g., mutable data structures). I have used F# in many performance-sensitive applications, and the fact that I can say “you know, inside this function, I’m going to use mutability, raw pointers, and iteration” has been a lifesaver in some places. But because it is a functional language, I can also abstract all that away and pretend that it is functional.
I understand why other FP folks dislike this approach. But the insistence on purity makes many problems artificially difficult. Debugging a lazily evaluated program is a nightmare. There are lots of times I want a well-behaved language but I am not willing to do CS research just to solve common algorithmic problems. The generally pragmatic streak from the SML family makes them easy to love.
If purity is a requirement for "real" functional programming, then OCaml or Clojure aren't functional. Regarding totality, even Haskell has partial functions and exceptions.
Both OCaml and Clojure are principled and well designed languages, but they are mostly evolutions of Lisp and ML from the 70s. That's not where functional programming is today. Both encourage a functional style, which is good. And maybe that's your definition of a "functional language". But I think that definition will get increasingly less useful over time.
Haskell. But there are other examples of "pure functional programming". And the state of the art is dependently typed languages, which are essentially theorem provers but can be used to extract working code.
Sure, Python has types as part of the syntax, but Python doesn't have types like Java, C#, etc. have types. They are not pervasive and the semantics are not locked down.
