The relationship between the Benelux sovereigns is obvious (first cousins): both are grandsons of King Leopold III of the Belgians and Queen Astrid, Princess of Sweden and Norway. Neither grandparent had any direct ties to the Habsburgs; but both descended from King Maximilian I of Bavaria -- like Hereditary Prince Alois of Liechtenstein. So the Wittelsbach connection is there, since Queen Elisabeth of the Belgians was born Duchess Elisabeth in Bavaria -- her sister (Duchess Marie Gabrielle) being an ancestor of Hereditary Princess Sophie.
The Braganza connection, then, would come from Infanta Maria Josefa of Portugal, who was the mother of those sisters. Her own sister, Infanta Maria Teresa, was an ancestor of Hereditary Prince Alois.
My question is: what are the genealogical ties between Queen Mathilde and Hereditary Princess Sophie?