The old pink "Isaac Allerton: Mayflower Families in Progress" (1990) has Isaac Allerton's daughter Mary who married John Newton, as family #19. This was accepted at the time Christine Clark became a member of the Society of Mayflower Descendants.
But The Mayflower Descendant (Vol 42, No 2, p 117-122) from July 1992 has an article by Barbara Lambert Merrick, Historian General of the Mayflower Society, entitled "Important Allerton/Brewster Corrections." Note this is The Mayflower Descendant not the Mayflower Quarterly. Mrs. Merrick describes the origin of the theory of Mary, an otherwise unknown daughter of Isaac Allerton Jr, based on the existence of a man named Allerton Newton, an heir named in the will of Isaac, with no relationship mentioned.
The key statement is on page 121 of the article is, "Therefore, it will be the stand of the Brewster Five generations Project that Isaac Allerton's known daughter, Sarah (Allerton) (Newton) Lee was the mother of Allerton Newton. The unproven lines of descent through a reputed daughter Mary and her Newton heirs will be eliminated from MFIP/Brewster [and Allerton]."
Since I am a descendant of John Newton, I copied the article in 1994. William Newton, son of John Newton and Mary his wife, is mentioned in the article but has no tie to the Allertons, a conclusion supported by the fact that Isaac Allerton did not mention him as a grandson in his will.
Many online genealogies continue to show Mary Allerton as the wife of John Newton, obviously because once a name is linked to one's family tree, it is challenging to keep up with research and impossible to delete that name.
Text: Merrick, Barbara Lambert, Historian General of the Mayflower Society. "Important Allerton/Brewster Corrections." The Mayflower Descendant (Vol 42, No 2, p 117-122), July 1992.