So are lots of data types, but those are still useful in FP.
"An odd habit of functional programmers: when confronted with a nice, but clearly imperative way of structuring a program, they will often declare that this technique is in fact functional." (https://twitter.com/yminsky/status/950883335324225541)
and then
"Case in point: structuring a program as an imperative, deterministic state machine, where the state is determined fully by the state machine logic plus the sequence of transactions." (https://twitter.com/yminsky/status/950883598189686784)
Only after sometime around 2010. Before that it was mostly Lisp and Scheme. Sometime around then, the trend around Haskell, purity, and co overtook them as what people mean when they talk about FP.
State machines are also intrinsically stateful, that should be obvious.