the other branches of the house of Orange also claimed the Orange title through female lines, so it would have been hypocritical if they objected to the Orange-Nassau female-line title inheritance (although hypocrisy is not exactly unheard of when it comes to title disputes…).
A lot of them.
The principality of Orange passed to female monarchs or through female lines numerous times before reaching the Nassaus. Princess Tiburge reigned over Orange in the late 12th century, and her daughter Tiburge’s son Guillaume of Baux succeeded as Prince of Orange. Their descendant Marie of Baux reigned as Princess of Orange from 1393 to 1417, and while Marie’s son was her heir, she named her daughter Alix of Chalon as the spare in her testament. Marie’s descendant Philibert of Chalon reigned as Prince of Orange from 1502 to 1530 and was succeeded by his sister Claude’s son René of Chalon.
René of Chalon, Prince of Orange, never married, and he appointed his
paternal cousin Guillaume of Nassau (“William the Silent”) to succeed him as reigning Prince of Orange. This broke the direct prince(ss)ly line and created the house of Orange-Nassau.
The Dukes of Longueville and other French nobles who descended from Alix of Chalon (the daughter of Princess Marie, mentioned above) disputed the Nassaus’ succession to Orange and asserted their claim to the Principality of Orange by right of their descent from Lady Alix.
Meanwhile, King William III of Great Britain and Ireland, reigning Prince of Orange, died childless. He appointed his paternal aunt Princess Albertine-Agnes of Orange’s son, Count Johan Willem Friso of Nassau (who was also distantly related to him in male line), to succeed him as Prince of Orange. Johan Willem Friso is the progenitor of the present-day Royal House of the Netherlands.
However, Princess Albertine-Agnes was not the eldest daughter of the Orange-Nassau family. Her older sister, Princess Louise-Henriette of Orange, had descendants who became the royal family of Prussia. Thus, the Prussian kings disputed the succession and laid claim to the Principality of Orange by right of their descent from Princess Louise-Henriette.
(All the claims were unsuccessful because the King of France conquered the Principality of Orange upon William III’s death, and it remains a part of France to this day.)