Princess Beatrice and Princess Eugenie have NOT been stripped of their royal titles. Despite their father Prince Andrew being legally stripped of his princely status and the Duke of York title due to his controversies, both daughters retain their royal styles as princesses.
Their continued use of titles is based on the 1917 Letters Patent issued by King George V, which grants royal titles to the children of sons of the reigning monarch. Since Beatrice and Eugenie are male-line grandchildren of Queen Elizabeth II, they keep their titles according to this longstanding royal protocol.
The princesses do not perform official royal duties, having full-time careers outside the core royal family roles. They maintain a certain royal presence, being involved in charity work and attending some family events but largely live private lives. Following Prince Andrew’s title removal, it was confirmed by the palace that Beatrice and Eugenie would remain princesses and retain their “Her Royal Highness” styles.
Therefore, while Prince Andrew faces severe restrictions and loss of titles, his daughters' royal status remains intact for now, consistent with historic precedent and current royal policy.