Whether the persona they show is more or less like their true self depends on what you consider their "true self" to be. If you look at any sort of school of thought which embraced asceticism, you'll find people that, because we experience way more emotional changes over a day than we experience changes on our set of desired behaviors, came to think of emotions as unreal, annoying distractions. The major example of this kind of thinking being Stoicism, but really, it just of sort of permeated every other pre-modern society.

So yeah, I don't think it's a "puritan/evangelical" thing. It's more of a "anything but contemporary urban society" thing.