For example, in a North Carolina family history book of a prominent family not normally considered "Jewish" by the family, nor by outsiders to that family; their paid professional genealogist, to everyone's surprise, found they had a (pre-1900's if I recall correctly) Jewish ancestor. In this case the term "cryptic Jewish" ancestry meant the descendants themselves did not know of their Jewish heritage.
In the Salisbury, Rowan County genealogical section of the public Library, I found a manuscript diary of, I believe it was an early to mid-1800's Protestant minister which recorded that he bought some used furniture from "that Jew..." (I think he used a term like that) "...Goodman". I think that was the family name; whatever it was I'd never known that to be other than a Protestant family. Though subjective, I felt the writer used the term "that Jew" with hostility, rather than more neutrally such as in, to "Jew a man down" (get a good price). I see like terms such as (un-earned) "Luck of an Irishman", "Indian-giver", etc., as being negative, neutral, or positive (a compliment) based on the (good or bad, or neutral) intent of the term user. In this case, as the family is traditionally considered Protestant, the diarist implied Mr. (Goodman?) was cryptic (understandable) his Jewishness.
I've also heard, many times, the term "cryptic Jews" used in the context of historically Jewish heritage people in Spain who pretended to be Catholics (possibly some Protestants did the same, for the same reasons) in order to escape the Spanish Inquisition. But as the United States never had a Spanish Inquisition (other faults, yes); this would not be an American context use of the term.