Here's my random thought about Charlene and the Privilège du blanc:
The Vatican has relaxed dress codes for papal audiences in the last decade or so, and thus extended privilege to the Princess of Monaco and Charlene was perfectly within protocol to wear white in January. However, Tuesday was an papal inauguration, and, much like a coronation, they stuck to the old rules for such an important and traditional event. Maybe Charlene was technically allowed to wear, but decided keep in line with tradition for the big event.