Borrowed Ideas

"Every religion in Earth's past, no matter how exclusive in theory, had had influential thinkers who were willing to borrow ideas from contemporary rivals."
-Poul Anderson, "The Three-Cornered Wheel" IN Anderson, The Van Rijn Method (Riverdale, NY, 2009), pp. 199-261 AT VI, p. 251.

Mani claimed to synthesize three traditions. See here.
The Fourth Evangelist borrowed the Logos from Greek philosophy.
Zen synthesizes Buddhism and Taoism.

Ideas also proliferate. See Enforced Uniformity Or Continued Diversity for arguments that 1+1=3 or even that 1+1=7.

Like the Jesuit in Anderson's "The Word to Space," Martin Schuster in "The Three-Cornered Wheel" aims to subvert a theocracy by inciting:

reinterpretations;
reformations;
counterreformations;
revelations;
new doctrines;
fundamentalist reactions;
etc.

Aycharaych also aimed to build such divisions into a new jihad.

I think that the heirs of any tradition can:

conserve their idea of the tradition but in a changing context, thus changing the tradition without realizing it;

reinterpret the tradition which means rejecting conservative interpretations and even sometimes the essence of the tradition;

reject the tradition although they remain influenced by whatever they reject.

In all cases, continuity and change are combined.

There is continuity of monarchy in "The King is dead; long live the King" and continuity of ordered society in "The office of King is abolished; long live the Republic."