No, players may not play cards or take free actions, except when it is their turn.
From the Online FAQ , and the Monty Python Fluxx rule book.
Q: Do I get to play any cards or take any actions when it's not my turn?
A: When it's someone else's turn, there's not much you get to do -- there are no cards you can play out of turn. But you will sometimes need to make minor decisions and perform card maintenance during other players' turns. For example, if someone plays a Hand Limit and you have more cards in your hand than are allowed, you'll need to decide what to keep and what to discard.
Further evidence that supports this conclusion is that the Pirate Fluxx and Star Fluxx rules list a new card type Surprise that can be played out of turn (image of purple Surprise cards with Lightning Bolt symbol from Pirate Fluxx.
Q: Do I get to play any cards or take any actions when it not my turn?
A: When it's someone else's turn, there's not much you get to do -- unless you have a Surprise (the only type of card you can play out of turn) . But you will sometimes need to make minor decisions and perform card maintenance during other players' turns. For example, if someone plays a Hand Limit and you have more cards in your hand than are allowed, you'll need to decide what to keep and what to discard.
The release date of Pirate/Star Fluxx is after Monty Python Fluxx, so it makes sense that until the release of Pirate Fluxx, no cards could be played out of turn, but when those sets were released with the new Surprise card type the rules specifically called that card type as an exception.
Monty Python Fluxx (Released October 2008; mostly themed after Monty Python and the Holy Grail, with selected elements from the Monty Python's Flying Circus TV series). [...]
Pirate Fluxx (Released February 2011)
Star Fluxx (Released September 30, 2011).
The Pirate Fluxx online page even notes that:
Yarr! Grab yer Cutlass! Pirates have taken over Fluxx, the ever-changing card game, and their rules be new and strange. There'll be times ye must Talk Like A Pirate, and rules about how ye can Plunder from yer mates. But the most excitin' treasure fer Fluxx fans new and old is the Surprise! - a new card type that you play out of turn! [...]