I don't know the author, and I cannot vouch for his knowledgeability on Jewish history, but it appears the author was using the phrase "pharisaical persuasion" to describe religious hypocrites.
If the author's point was to warn believers against religious hypocrites, that was accomplished in the excerpt provided.
""But watch out for the leaven of the Pharisees and Sadducees.” Then they grasped that he said to watch out, not for the leaven of bread, but for the teaching of the Pharisees and Sadducees."
Jesus wasn't just preaching to literal Jews about literal Jews. His words were for us today too, and the "Pharisees" are figurative. (How many of us today know any literal Pharisees?) God is Our Father. We don't need some clergy class to stand in between us.
"For by him we have life and move and exist, even as some of your own poets have said, ‘For we are also his children.'"