Here's my take on it.:
Worf became a Federation citizen when he was adopted by the Rozhenkos and for most of his life has the 21st century equivalent of "dual citizenship." Being a Federation citizen grants him rights and protections provided by Federation Law. I also think being a Starfleet Officer gives a person Federation citizenship and protection even if their homeplanet is not in the Federation (like Nog or Ro). In "Sins of the Father" Captain Picard refused to allow Worf to be put to death because he is a Starfleet Officer and a member of his crew ..
Conversely, I think there is a "citizenship" of sorts within the Klingon Empire, but I think it is done through membership to a House. When Worf accepts discommendation in "Sins of the Father" I see that as the Klingon version of revoking his citizenship. He is now an outsider and no longer one of them. He gets his "citizenship" back in Redemption but loses it again in Way of the Warrior (this guy just cannot keep it together!) In the same way, when Worf marries Jadzia, she joins Martok's house as well and becomes a "citizen' of the Empire, with all the rights and responsibilities therein.