That's arguably very different, though. In Paranoia you're never supposed to mention that your character's a member of a secret society. Or that they're a mutant, for that matter (unless they've registered).
I agree that a lot depends on implementation. The 5e APs and AL stuff seems almost desperate to get PCs involved in factions and push them hard but bluntly. PFS has them but they’re largely irrelevant in play.
But there was a D&D module decades ago that made political factions really stand out and draw the PCs in. Blood of the Yakuza for OA was awesome this way. Players could easily let their PCs get sucked into the underlying political conflict and it didn’t feel either forced or overly blunt.
Not all factions are membership focused nor even organized. Agnosticism is faction-like, functionally a faction, in that it has a strong political and social impact when it becomes a significant chunk of the population, but has no organization, no major commonality other than lack of participation in religion. And the relationship expressed with visible members can shape the effect upon large groups due to shared bias.
In short, you just declared membership in a faction that doesn't care that you disdain membership therein.