The "privilege du blanc" is for HRH and the ones who do not have this privilege are HSH. A Royal Highness is higher than a Serene Highness. Reigning Catholic Queens, Catholic Queens Consort, and Catholic Grand Duchesses from Spain, Belgium and Luxembourg, who are HRH, have the privilege and Princesses and Princesses Consort from Liechtenstein and Monaco, who are HSH, do not. The late Princess Grace of Monaco, a Roman Catholic from birth, was HSH and never granted the "privilege du blanc."
In 2005 at Pope Benedict XVI's inaugural mass and in 2006 María Teresa, Princess Consort of Luxembourg wore white when meeting the Pope. Maria Theresa is a Grand Duchess and her title is, Her Royal Highness The Hereditary Grand Duchess of Luxembourg
So Perhaps Monaco asked for the "privilege du blanc."
In April 2006 Cherie Blair, wife of the Prime Minister of the United Kingdom surprised many by wearing all-white to meet the Pope. When women meet the Pontiff they should wear black, preferably with a black veil, or mantilla. Cherie Blair is not a royal.
When Angela Merkel, the German chancellor, wore black, but omitted the veil. Wearing all-white to meet the Pope is a privilege normally reserved for Catholic Queens.