Ask the Conversos and Moriscos of late-mediaeval Spain. They changed their religion, and STILL got inquisited.

As for the Golden Ratio, according to at least one definition of it (the number of which the square is one more than the number itself), there is ANOTHER Golden Ratio, -0.618034 or so, the negaitive root of the same equation. I don't know if it has any other properties, and I'm not mathematician enough to find out.