No, what I think is happening is that there is a regular-ass religion with a god that she was raised in. Then she hears the system voice and then goes "This must be god!"
And I DON'T think the voice is telling her to kill people. The way it seems is the voice tells her about skills, she sees one called Taboo and thinks "God is telling me this is taboo. So it's forbidden. So everyone that has it must die." because she's a fanatical psycho.
Are we sure the locals even HAVE the voice? Maybe the system is only accessible by otherworlders.
And even if they did, without our real world video game context, yes, locals would assume the system is a god.
In JRPGs though, "Hero" is usually a class. Especially in Dragon Quest, which is the main influence for all these isekai.