the big example is Rome, which (often rather ignored by mainstream discourse) was a deeply religious city-and-state whose very administration & political traditions were wrapped in their religious activity. civic-religion in that it was specific to Rome the City, but to be pedantic its later civil-religion when it starts to concern much more territory than the city itself.

speaking of abrahamic religion there are a few parallels in the transition of civil-religious tradition to monotheism, particularly in Rome---but the theological nature of the abrahamic traditions differs quite substantially because they're not based on oral traditions but a written set of texts & the discourse around/interpretation thereof.

and also just because hellenistic 'polytheism' could act inclusively doesn't preclude its religions and followers from being very intolerant. For every Zeus-Ammon & Mithras you get an Elagabal, a Maccabees, a Carthage (i.e. times hellenistic folk did religious intolerance)