I am not saying anything. Please see the Manusmriti's law 10.8 & decide yourself.
The law says that the child born out of a Brahmin father and Sudra mother is a Sudra (Nishad by caste). Now you apply this theory to the lineage as below and see what we get :
i) Father - Shaktimuni (Brahmin ... son of sage Vashishtha) + Mother (a Chaandala woman (I coouldn't find her name anywhere) ===> Son, Maharishi Parashar
So, Maharishi Parashar as per Manu's 10.8 is a Nishad by caste i.e. a Sudra.
ii) Father - Maharishi Parashar (a Sudra by the above deduction) + Mother (Satyavati, a Sudra) ===> Son, Vedvyas
A Sudra father and a Sudra mother will always give a Sudra child. So, Maharishi Vedyas becomes a Sudra. Even if we consider Maharishi Parashar a Brahmin, Maharishi Vedvyas cannot escape being branded as a Sudra by Manu's Law given above as his mother was a Sudra.
iii) Father - Maharishi Vedvyas ( A Sudra, as deduced above) + mother, Ambika ( a Kshatriya) ===> Son, Dhritrashtra,
Father - Maharishi Vedvyas + mother (Ambalika, a Kshatriya woman) ===> Son, Pandu
Father - Maharishi Vedvyas + mother (maidservant of Ambika, a Sudra) ===> Son, Vidura
Now in the above realtionship, as the father is a sudra ( as deduced in ii) above, all the three sons must be Sudras and then their clan cannot be anything but Sudras.