There is a bit of debate about how to translate πολίτευμα in Philippians 3:20. In modern commentaries, the translation ‘citizenship’ is usually rejected because of its weak attestation in ancient texts.
Reumann in his commentary provides a helpful survey of the discussion, and argues that to translate this word some ‘reflection of “state, constitutive government,” etc., is needed, but also of the social world of clubs, guilds, and (religious) associations’. He settles for ‘civic association’.
The problem I see with translating πολίτευμα as ‘civic association’ is that, in English, it is quite an un-intuitive phrase. Any perceived ‘governance’ by a ‘civic association’ would be, at most, minimal.
It may be that the idea of ‘citizenship’, at least in modern English usage, actually has a stronger sense of identity and value than the ancient concept which was more associated with rights and privileges. So, for example, in modern-day Australia, the term ‘un-Australian’ is used of someone who acts in a way that goes against the (perceived) values of the Australian community (e.g. burning an Australian flag or, worse, supporting the England cricket team). This, admittedly, colloquial term reflects the fact that citizenship is being increasingly conceived in terms of behaviour and values which govern the community at a deeper way than governments can. So, even a resident of a country is criticized if they do not live according to the values of the country (cf. the criticism of immigrants who do not learn English when they come to the UK). Perhaps, then, as an English translation, ‘citizenship’, understood in this more modern, fluid sense captures the sense of the Greek word as an association with governance over its members.