Fans picked up the royal debate in the replies. One fan argued that Luke was a prince, since Leia is royalty through their biological mother, Padmé Amidala (Natalie Portman). However, another pointed out that Padmé was elected as queen, and her royal status wasn’t an inheritable title passed down to her kids. Another fan continued on that theme, saying it’s true that queens were elected in Naboo. Padmé took on the role of senator at the request of the new queen. Leia’s title of princess was through her adoptive mother, Queen Breha Organa of Alderaan, wife of Senator Bail. Hence, Luke is not royal.
Article source: https://www.cinemablend.com/news/2465825/mark-hamill-reveals-recurring-star-wars-fight-he-had-with-carrie-fisher