Just to be contrary -
Why would "citizenship" mean the same thing in the 24th century as it does now? And why would it mean anything to Worf? He's a Klingon. As Timo points out, what does "citizen" mean in Klingon society? Either you're a Klingon, or you're not. If you are, you're subject to Klingon laws, regardless of where you live or what some form in some computer says.
The UFP might have a definition of "citizen", but we never heard of it, did we? Citizens of the Federation were pretty much defined by their species. If you're a Vulcan, you're a citizen of the Federation. If you're not a member of a species that was a member society of the UFP, what are you? Can you be a citizen of the UFP? Are there naturalization procedures to follow? We never heard of them. No one was ever identified as a Federation citizen that wasn't obviously a member of the known Federation member societies. Can Worf be a citizen of the UFP? To Klingons, renouncing citizenship could be like pretending you don't have forehead ridges - it's impossible to deny the existence of ridges, and trying to do so would indicate some sort of delusion on the part of the denier.
As for requiring citizenship to hold an office for the UFP, why would that be necessary? I reject the notion that everything about the UFP is descended directly from the US legal structure. Particularly when dealing with the Klingons, who may not have a notion of "citzenship", why would the UFP worry about the citizenship of the ambassador to the Klingons? Perhaps the UFP regularly uses intermediaries in diplomatic relations with the Klingon Empire - we don't know that Curzon Dax, or Trills in general, are UFP members, yet there was no doubt that Dax acted as an ambassador for the UFP to the Klingons.
What of the other large empires of the Alpha Quadrant? Both the Romulans and the Cardassians were known to have subject races - the Remans and the Bajorans. What was the legal status of those species? Were they Romulan and Cardassian citizens (respectively) or just subjugated races with no legal standing in their respective societies?
It's too bad the topic of citizenship didn't come up more often in some of the Trek shows, as it would be an interesting to see how a multispecies interstellar polity would treat the matter.