Since I barely knew what I was talking about, I asked my former (and now retired) Regent University colleague, Joe Kickasola. His detailed--and very interesting--response is reproduced below:
(1) The usual Greek word for “citizenship” is politeia (Ac.22:28), but in the NT politeuma (Plp.3:20) is used as equivalent to politeia. So, “citizenship” is a proper rendering at Php.3:20.
(2) The reason Paul at Php.3:20 uses politeuma (the action form of the noun, “the administration of a commonwealth,” or “commonwealth”) instead of the also correct politeia (the stative form of the noun, “the state of being a citizen,” or “citizenship”) is that he is punning on what he had already said at Php.1:27, where he used the action form of the verb, politeuomai, “to order one’s life and conduct, to live with certain habits and principles”). Php.1:27 is correctly rendered into English as “(Only) conduct yourselves (politeuesthe) (worthily of the gospel of Christ).” Paul is matching the later action form of the noun with the earlier action form of the verb, i.e. politeu-ma with politeu-omai.
(3) This understanding of Php.3:20 & 1:27 is actually confirmed by both the Latin of the Vulgate (conversatio) and the English of the KJV (conversation), neither of which have a reference to speaking/talking. The Latin root vert-are means “to turn.” The frequentative form of this verb is con-vert-are, “to turn about with, to conduct oneself with others,” and the frequentative form of the noun from this verb is conversatio-onis, which lends to the Old English the word “conversation, manner of living, public behavior.” The English word “conversation,” as is well known, but not in view here in Philippians, includes such social behavior as talk/speaking, as is evidenced in our derived word “to converse,” as well as the legal terminology “carnal conversation” which means adultery, which meaning of conversation is more the sense in Philippians here referring to social/public behavior.
(4) To conclude, “conduct yourselves” in a manner worthy of Christ (rather than worthy of Caesar) at the Roman colony of Philippi (1:27) is confirmed by our “citizenship in the behavioral sense” being in heaven, not in the political or ethnic sense of Rome, because of the glorified body that Christ will give us at His Return (3:20-21).
(5) Lastly, as to the Italian translation of patria (native country, fatherland, ethnic commonwealth), you are probably right as to why this ethnic term was favored over cittadinanza (the legal term for “citizenship”), given the different kind of political unions existing between Italy (ethnic) and the U.S. (legal). But since every “citizen” (cittadino in Italian) in the Roman colony of Philippi shared a common cittadinanza (citizenship), I would have favored cittadinanza to patria, in that neither the legal nor the ethnic factors are in view here, but rather the behavioral aspect, i.e. conduct worthy both of Christ and His heavenly kingdom.