The manifesto itself isn't spelled out in any great detail. It's discussed by a number of the characters (see below) and we can kinda see the edges of it but at its heart, the power of the document appears come from its celebrity value; that it was written by a descendant of the Tyrant, arguably the most powerful single individual in the galaxy's history.
Its effects seem to be transformative, well beyond the words themselves. Odrade has used her talents as an Atreides to create the literary equivalent of an earworm.
Mirlat will have to be dealt with, Waff thought. He lifted the
manifesto from his lap and read the first line aloud: “In the
beginning was the word and the word was God.”
Waff describes it as calling religions (save their own) into question, presumably because theirs is the only major religion to herald Leto II as a messenger of the true God:
“Every powindah religion is called into question by this manifesto,”
Waff said. “Every faith except ours is left hanging in limbo.”
Teg has read it. It's pretty densely worded:
“Just as the universe is created by the participation of
consciousness, the prescient human carries that creative faculty to
its ultimate extreme. This was the profoundly misunderstood power of
the Atreides bastard, the power that he transmitted to his son, the
Tyrant.”
It evidently discusses the power of prophecy:
In a deep and portentous tone, Odrade said: “The Manifesto raises
questions that all must address, believers and non-believers alike.”
“What has all this to do with the Holy Child?” Tuek demanded. “You
told me we must meet on matters concerning—”
Before Tuek could find words, Waff locked eyes with Odrade and
responded in a way he knew she would interpret correctly. Odrade could
do no less, being who she was.
“The error of prescience,” Waff said. “Isn’t that what this document
calls it? Isn’t that where it says the mind of the believer
stagnates?”
It's decidedly heretical:
She had to keep Tuek’s attention on the document that disturbed him so
much. She paraphrased from the Manifesto: “Your will and your
faith—your belief system—dominate your universe.”
Tuek recognized the words. He had read the terrible document. This
Manifesto said God and all of His works were no more than human
creations. He wondered how he should respond. No High Priest could let
such a thing go unchallenged.
