That's not what a few google results tell me. It seems, in India the answer is definitely No, while in Iran the answer is Maybe. The Indian No is presumably to stop the religion dissipating, while the Iranian Maybe is a kind of "well, they're ancestors were probably Z anyway." In the West, people would follow the notion that there is a spiritual supermarket, and you just choose which flavour suits you, so it's a Yes there.
I don't prescribe to your Turing idea. People are not black box machines pretending to be humans. Rachel Dolezal was not black on one day and white on another.