I think you are right to see Popper's typology as a kind of ideological argument rather than a relatively disinterested labelling that could be applied to a large number of cases throughout history. In effect, Popper is arguing teleologically that Western liberal democracy has arrived at a new kind of "open" society, and that all other societies are in relative terms "closed". (This also lets him get in a dig against the socialist regimes of the Cold War by implying they are backward.)

However, I could see a way to use his distinction in a way that was less tied to contemporary Western liberalism. I don't think it is terribly useful as a way to characterize entire societies in the past. Say, for example, all Greek city-states vs. the Achaemenid Empire around the time of Xerxes? If "open" and "closed" have any useful meaning at all, they have to address both the character of a particular government and legal system AND the sociocultural life of particular communities. They have to be about more than just an allowance for formal dissent against the sovereign, but instead some general dispositional view of political and social life that exalts or supports diversity of philosophical, spiritual, and cultural practice.

So I would say less "societies" and more "communities", if I were trying to detach the language from Popper's ideological usage of it. In global history, have there been communities which are more 'open': more accepting of a heterogenous range of philosophical, political, spiritual and cultural practices, that protect or exalt linguistic diversity, etc.? Have there been those which are more closed, where that sense of 'closed' is not merely a description of circumstance but is instead a strong disposition that threads through most political and social structures within a community? (E.g., calling a geographically isolated community that has few interactions with others 'closed' is kind of tautological: it's closed because of circumstance, not disposition or structure.)

In this sense, yes, I think you can identify communities historically that were more markedly 'open' or 'closed' (and which had a general reputation within their society or region for being that way) and that you can apply this kind of language usefully all the way into the present day. It would take some care to build out a full list of identifying characteristics of openness and closed so that it didn't amount to a (usually) self-complimentary distinction between "good" and "bad". For example, you'd want evidence not only of religious, cultural and philosophical heterogeneity in a particular city or community but some evidence that this heterogeneity was sanctioned by legal and political institutions--you might find cities or communities that had this kind of diversity but where that was constantly threatened by a ruling elite who were committed to a more 'closed' vision of their sovereignty, and then you really wouldn't want to call it an open community.