A Diana who doesn't worship her gods is as completely off-theme as a Batman who is not self-made peak-human, but instead a powered hero.
Have to disagree with you on that. Diana stopping her worship of the gods does not change her origin or her past. It doesn't mean that she never worshipped the gods, it's changing her relationship with them in the present and (presumably) the future. That's more akin to a change in Batman's behaviour or MO, like Batman getting violent and erratic after Jason was killed and Babs was shot. Or like Bruce Wayne going out and buying a gun.