Do certain religious or racial based archetypes have to be played straight?

[Reduxist]

For example, the Hag of Gyronna archetype implies you worship Gyronna. But you could easily play as a Hag of Gyronna worshipping Mestama instead.

[cuatroespada]

RAW there is no requirement that you worship Gyronna to take this archetype, so you could worship Mestama i suppose, but i would run it by my GM first if i were you. i'm not sure if there's an official ruling for it in PFS, but i'd expect some GMs would want your mechanics to line up with Golarion lore so expect table variation unless there is an official ruling on that sort of thing. i think it would fall under refluffing and i'm not sure if they put the kibosh on all refluffing or just certain kinds of refluffing.

edit: some archetypes (like scarred witch doctor) actually do have racial requirements, etc. so for those you actually need to meet the requirements.

[Kalindlara]

My recommendation: talk to your GM about it. ^_^

(This is a completely sincere and serious post, with no sarcasm or dismissiveness intended. Tone is hard to convey on the Internet.)

[Arachnofiend]

It used to be more common for these themed archetypes to have strict requirements like being this race or worshiping that deity; Paizo generally stopped doing that (with some exceptions) because it was pretty unpopular.

If the archetype has a requirement the archetype will be very specific about that in its description. Otherwise, refluff away.