May I suggest that the subject of the letter is not the religious beliefs of the Christians, but the utter lack of stability or principle of the Egyptians?
For the Egyptians, as you know well enough, are puffed up, madmen,20 boastful, doers of injury, and, in fact, liars and without restraint, always craving something new, even in their popular songs, writers of verse, makers of epigrams, astrologers, soothsayers, quacksalvers. 5 Among them, indeed, are Christians and Samaritans and those who are always ill-pleased by the present, though enjoying unbounded liberty. 6 But, lest any Egyptian be angry with me, thinking that what I have set forth in writing is solely my own, I will cite one of Hadrian's letters, taken from the works of his freedman Phlegon,21 which fully reveals the character of the Egyptians.
"From Hadrian Augustus to Servianus22 the consul, greeting. The land of Egypt, the praises of which you have been recounting to me, my dear Servianus, I have found to be wholly light-minded, unstable, and blown about by every breath of rumour. 2 There those who worship Serapis are, in fact, Christians, and those who call themselves bishops of Christ are, in fact, devotees of Serapis. 3 There is no chief of the Jewish synagogue, no Samaritan, no Christian presbyter, who is not an astrologer, a soothsayer, or an anointer. 4 Even the Patriarch himself, when he comes to Egypt, is forced by some to worship Serapis, p401by others to worship Christ. 5 They are a folk most seditious, most deceitful, most given to injury; but their city is prosperous, rich, and fruitful, and in it no one is idle. 6 Some are blowers of glass, others makers of paper, all are at least weavers of linen23 or seem to belong to one craft or another; the lame have their occupations, the eunuchs have theirs, the blind have theirs, and not even those whose hands are crippled are idle. 7 Their only god is money, and this the Christians, the Jews, and, in fact, all nations adore. And would that this city had a better character, for indeed it is worthy by reason of its richness and by reason of its size to hold the chief place in the whole of Egypt....
The point is that the Egyptians take nothing seriously. He lists groups known to be mutually hostile and then says the Egyptians claim to be both: "... those who worship Serapis are, in fact, Christians, and those who call themselves bishops of Christ are, in fact, devotees of Serapis. 3 There is no chief of the Jewish synagogue, no Samaritan, no Christian presbyter, who is not an astrologer, a soothsayer, or an anointer."
This is not saying that "Christian" can mean "worshipper of Serapis". This is saying that Egyptians may call themselves all sorts of things, but don't worship Christ, nor indeed Serapis. The Jews are not Jews, nor the Samaritans, nor the Christians, because they're all practising magic! "Their only god is money, and this the Christians, the Jews, and, in fact, all nations adore."
All the names, all the cults, in fact, have been emptied of meaning, he says, because the real religion of the Egyptians is money.
All the best,