I think it's authentic and I don't think there is anything to suggest that Christians and worshippers of Serapis were ever confused. Hadrian appears to be saying that Egyptians were unreliable and superstitious, not that Serapis and Christ were the same thing.
As I pointed out a long time before there are
two versions of Hadrian letter:
"Egypt, which you commended to me, my dearest Servianus, I have found to be wholly fickle and inconsistent, and continually wafted about by every breath of fame.
The worshipers of Serapis (here) are called Christians , and those who are devoted to the god Serapis (I find), call themselves Bishops of Christ are, in fact, devotees of Serapis. There is no chief of the Jewish synagogue, no Samaritan, no
Christian presbyter, who is not an astrologer, a soothsayer, or an anointer. Even the Patriarch himself, when he comes to Egypt, is forced by some to worship Serapis, by others to worship
Christ. 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" - Giles,
Hebrew and Christian Records, vol. II, p86, 1877
Now compare it to this version:
"Egypt, which you commended to me, my dearest Servianus, I have found to be wholly fickle and inconsistent, and continually wafted about by every breath of fame.
The worshipers of Serapis (here) are called Chrestians , and those who are devoted to the god Serapis (I find), call themselves Bishops of Chrestus are, in fact, devotees of Serapis. There is no chief of the Jewish synagogue, no Samaritan, no
Chrestian presbyter, who is not an astrologer, a soothsayer, or an anointer. Even the Patriarch himself, when he comes to Egypt, is forced by some to worship Serapis, by others to worship
Chrestus. 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" - Drews, Arthur (1912)
The witnesses to the historicity of Jesus
Note the hilited part. In Giles version it is
expressly stated that "the worshipers of Serapis (Osiris) are called Christians" ie Christians and worshippers of Serapis were confused with each other as
we are expressly told they are the same group!
It is only in the Drews version that the confusion falls a way. But then we are shown there was some tampering even at this stage of the game. Also note that "Chrestus" in addition to be a name could and was used as a
title going clear back to the 5th century BCE (Mitchell, James Barr (1880)
Chrestos: a religious epithet; its import and influence;
Pleket, H.W.; Stroud, R.S.. "Egypt. Funerary epithets in Egypt.(26-1702)." Supplementum Epigraphicum Graecum. Current editors: A. T. R.S. R.A. Chaniotis Corsten Stroud Tybout. Brill Online, 2013.
Dositheos the Samaritan was claimed to have "pretended" to be the Christ (ie used the title) by Origen. "Contra Celsum," i. 57, vi. 11; in Matth. Comm. ser. xxxiii.; "Homil." xxv. in Lucam; "De Principiis," iv. 17.) Clement of Rome, l.c. ii. 8; several passages in Origen; Epiphanius, l.c. and "The Dead Sea Scrolls and Prmitive Christianity", Jean Danielou, p. 95-96, 1958, Mentor edition 1962 all put him
before Simon of Peraea who died in
4 BCE but Eusebius in Ecclesiastical History, iv. 22, § 5 put him
after Simon of Peraea.
Pseudo-Clementine Recognitions and Homilies hints that Simon Magus many have used the title "Christ" as well.
So from the Christians own writings they were saying or implying there were at least two other people used the title "Christ"
I don't think there is any reason to doubt that Christianity was spreading through the Roman Empire in the early years of the 2nd Century; How did that happen?
The same way the Luddites spread throughout England in the 19th century: social political reasons.