There are traditionalists who do not accept the Luminous Mysteries because of the history of how the Rosary came about.
The Rosary has been called *Mary’s Psalter * because it came about as a way for laity to mimic religious order members’ practice of praying the Book of Psalms (a copy of this is called a psalter), which comprises 150 psalms. Three sets of five mysteries with 10 Hail Mary’s each equals 150 Hail Mary’s Adding the Luminous Mysteries makes the Hail Mary’s total 200, which in the view of some traditionalists ruins the prayer because it ruins its original purpose as a Psalter.
But again the Luminous Mysteries are not strictly required in any way. If you read the original apostolic letter of Pope John Paul II, Rosarium Virginis Mariae, he mentions the mysteries simply as a suggestion. The Rosary Confraternity does not include these mysteries in their requirements for weekly rosaries. Finally, the Rosary is a private devotion, you can pray it however you like as long as you do it with reverence and love for God.