Like Dylan Sakic, I’d need a lot more context, but here’s a stab.
Καθώς πρέπει is a calque of French comme il faut, “as it should be done”. It refers to social propriety, observing social etiquette, but it has an intense connotation of hypocrisy and stuffiness; it’s the kind of thing that “bourgeois” gets inevitably prefixed to.
Why are you picking up a Greek Orthodox angle to it? Presumably because the Orthodox Church is the repository of social conservatism in Greece, especially now that Greece is no longer a traditional society.