But again, a genuine CoP (in the cognitive anthropological sense) is not quite the same as a social club which just refers to itself as a "community" as an excuse for engaging in groupthink and petty politics.

Ah, I see you are familiar with the Connotation Game! For the sake of clarity, though, I'd recommend you phrase your entries like this:

We are a community.

You guys are a social club.

They are a clique.