I'd say that " pure Functional programming" has become a no. But "Functional programming approach" has been subsumed into existing programming languages, e.g. records in Java. You get most of the benefit of FP while keeping all of the other good stuf from an imperative language.
What mainstream languages have a good suite of FP features though? If you try to write mostly pure code in Java I’m afraid you’re in for a bad time, despite the (big!) improvements of records and lambdas. Minimum viable FP starts at OCaml, F#, Scala and Closure, yet none of these are mainstream.
Functional programming means functions are first class citizens and can be constructed on the fly. Modern python, c++, rust, even java now do this.
Purity is a nice to have (and arguably rusts borrow system enforces a kind of purity).