Comments in secondary literature like the following clearly indicate that critics rather settle for an inexplicable breach of character in Martin Cunningham than question their understanding of the “shocking” adjective employed:
Although Martin Cunningham is more charitable towards Bloom, he still describes him as a 'perverted Jew'.
Bloom's racial difference is overtly displayed in this episode, and anti-Semitic slurs abound: Bloom is called a "perverted jew" by Martin Cunningham.
Martin Cunningham gives an unpardonable reply: “He's a perverted jew, says Martin”.
The OED allows for a reading that is much more in character with the Cunningham readers are familiar with from “Grace” and elsewhere in Ulysses:
pervert v. 3a: to turn (a person) away from a religious belief regarded as true, to one held to be false.
The following quotations make it quite clear that this meaning of the verb was indeed used and understood at the time:
Though the Church of Rome boasts of the accession to her high places of perverted Protestants, she does not love them, nor in ordinary sense, does she care to distinguish them.
Belfast News-Letter (1851) 24 November
He had been foretold by former prophets; and, as perverted Jews and Christians were at hand to confirm his words, and as the Bible was little known among the generality of his followers, such assurances were implicitly believed.
Sir William Muir, Life of Mahomet (1858), vol. I, p. lxx.
Surely not; the perverted Jews of the first Century were few indeed, and the new creed was soon cast out to take root in the more genial soil of Paganism.
Charles Voysey, Sermons preached (at St. George's hall, Langham place) during 1873 (1874)
This does not mean, of course, that Cunningham’s phrase could not have the meaning postulated by the critics above, but as the example below clearly illustrates it would hardly have passed the lips of our charitable Christian and prudent Castle clerk:
He wishes to make it clear that he did not attack the whole of Judaism; the accusation of ritual murder concerned only peculiarly perverted Jews.
"Twenty-Ninth Day of the Kieff Trial" in (London) Times (1913) 6 November
As these quotations from Exiles and Portrait show, Joyce was well aware of the relevant meaning of this word:1
Can you not hear her mocking me while I speak? You must know the voice, surely, the voice that called you the black protestant, the pervert'sdaughter.
Exiles, Act 1, p .26
But I am curious to know are you trying to make a convert of me or a pervert of yourself? (P, 271, V, 2428-30).
[OED - pervert n., sense 1: A person who has been perverted; spec. a person who has forsaken a doctrine or system regarded as true for one thought false (opposed to convert n. 1); an apostate.]
It is out of the question that Stephen Dedalus uses “pervert” in the OED’s sense 2 for the noun, as it would not only mean that Stephen offends Cranly in the crudest way imaginable, but also loses the contrast to “convert”:
A person whose sexual behaviour or inclinations are regarded as abnormal and unacceptable (OED).
Just as in "Grace" Martin Cunningham is the master of half-truths in Cyclops, as an attentive reader can discover in the Ithaca episode (17.1635-9). It was Bloom's father who "had been converted from the Israelitic faith and communion in 1865 by the society for promoting Christianity among the jews", not Bloom, who became a Roman Catholic "with a view to his matrimony in 1888" (17.1640). So Bloom was a perverted Protestant, if anything.