Each of the three, viz. Vaishnavism, Saivism, and Saktaism
generally have a common mythology, though they may vary on
the exact details. No Vaishnava denies that the tripurAntaka
or the one who appeared before Markandeya was Siva; no Saiva
denies that Krishna killed Kamsa; and the same goes for the
Saktas. Each will also agree that Vishnu, Siva, and Sakti are
beings or conceptions that are greater than earthly mortals.
Furthermore, the major sects among the Vaishnavas, Saivas,
and Saktas at least pay lip service to the Vedas, and the
names each use for worshipping the Divine are all mentioned
in the Vedas.
To claim that Vaishnavism, Saivism, and Saktaism are not
related is utter ignorance.